CN1844967A - Aspherical focusing lens - Google Patents
Aspherical focusing lens Download PDFInfo
- Publication number
- CN1844967A CN1844967A CNA200510034105XA CN200510034105A CN1844967A CN 1844967 A CN1844967 A CN 1844967A CN A200510034105X A CNA200510034105X A CN A200510034105XA CN 200510034105 A CN200510034105 A CN 200510034105A CN 1844967 A CN1844967 A CN 1844967A
- Authority
- CN
- China
- Prior art keywords
- focusing lens
- aspheric surface
- index
- refraction
- visual field
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Landscapes
- Lenses (AREA)
Abstract
The invention discloses an aspheric surface collective lens, which comprises the first aspheric surface and the second aspheric surface. Wherein the refractive index change is in 1D range; the first aspheric surface is fixed; the invention has at least 7 visual fields, to make the target ti zero of performance function (as formula), while wi is weight factor, m is optimized term number, ei is one optical aberration and ti is the target of one optical aberration value.
Description
[technical field]
The present invention relates to a kind of eyeglass, relate in particular to a kind of aspherical lens.
[background technology]
The eyeglass that present optical device such as optical read head, camera lens, lens are adopted generally has spheric glass or aspherical lens.
For spheric glass, because two refractive surface is the sphere form, so all be easier to man-hour making and add.Yet, the sphere that the center thick rim is thin is assembled eyeglass, along with the increase of (also claiming the number of degrees) of eyeglass index of refraction, the center of eyeglass 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 back focal distance 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):
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) formula, when material one timing of sphere convergence eyeglass, and the center of lens thickness t depends on R
1, R
2Value, then the index of refraction of eyeglass is just by R
1, R
2Decision, therefore, 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 will be big more, then the center thickness t of eyeglass will be big more, makes that the volume of whole eyeglass is bigger.Be used for camera lens if this sphere is assembled eyeglass, then can increase the volume of camera lens; If it is the farsightedness eyeglass that this sphere is assembled eyeglass, then both influenced attractive in appearancely, cause glasses wearer's discomfort again.
In addition, for eyeglass, 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 center inconsistent with the edge of picture and make the visual field become curved surface, 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 picture side dipped beam axle zone, and makes imaging generation barrel distortion or pincushion distortion, and this kind aberration makes imaging that the geometry change 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 F in the sagitta of arc field
S' (D), the image height of ideal image is MQ ', the image height of true imaging is MQ ", then:
Oblique fire astigmatism=F
T'-F
S'
By formula (1) as can be known, sphere is assembled eyeglass, 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, general spheric glass can't 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 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 Chinese patent application CN1212766A on March 31st, 1999, disclosed a kind 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 Chinese patent application CN1412604A on April 23rd, 2003, disclosed another kind of aspherical lens, wherein, at least one refractive surface of this aspherical lens is an aspheric surface, and this aspheric surface computing formula (2) adopts following form:
Z is the rise in surperficial somewhere in the formula, and c represents the curvature on aspheric surface summit, and r represents the distance from optical axis, a
1, a
2, a
3, a
4, a
5For aspheric high-order term is number.
In this aspheric surface formula, design aspherical lens and make the refractive surface symmetry though introduce the even item,, r has power 12 times in its formula, and the aspheric surface high-order term adopts 5 values for number.If have only an aspheric surface to carry out lens design, the above-mentioned three kinds of aberrations of difficult effectively elimination.If adopt two aspheric surface designs, then when the index of refraction of eyeglass changed, the aspheric surface design of two refractive surfaces all can change, and makes this aspherical lens make difficulty.
At present, aspherical lens is in optimization (aberration is minimized) design of eliminating aberration, generally be to eliminate aberration in some specific field angle, then the corresponding meeting of the aberration of other field angle becomes less, and wherein field angle is meant when picture side's deflecting light beams passes through rear focus and the angle of lens light axis.
For effectively eliminating the aberration of aspherical lens, adopt damped least square method to come the optimal design aspherical lens usually, earlier a definition performance function (3):
W wherein
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.
Be provided with an aspherical focusing lens, comprise first aspheric surface and second aspheric surface, wherein the first aspheric aspheric surface is number P
1, B
1, C
1, D
1, E
1, the second aspheric aspheric surface is number P
2, B
2, C
2, D
2, E
2, P wherein
1, P
2Be conic constant value (Conic Constant), B
1, C
1, D
1, E
1And B
2, C
2, D
2, E
2Be respectively first aspheric surface and the second aspheric high-order term and be number (High ordercoefficients).
When this aspherical focusing lens adopts the optimal design of five visual fields, as when adopting 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields to optimize, when wherein 1.0 visual fields are meant the eyeglass imaging, deflecting light beams is 30 degree by rear focus and lens light axis angle, and the parameter of establishing this aspherical focusing lens is as shown in table 1.
Table 1
Eyeglass index of refraction F v=14.00D, optic diameter DA=32mm, center thickness t=9.2mm | |||||
First aspheric surface | Second aspheric surface | ||||
Radius of curvature R 1(cm) | 26.27803 | Radius of curvature R 1(cm) | 50.45961 | ||
The quadric surface constant P 1 | -1.473379 | The quadric surface constant P 2 | -8.45988 | ||
The first aspheric aspheric surface is number | B 1 | 7.873608×10 -6 | The second aspheric aspheric surface is number | B 2 | -1.661063×10 -5 |
C 1 | -9.674923×10 -8 | C 2 | -3.048883×10 -8 | ||
D 1 | 4.748931×10 -10 | D 2 | -3.625959×10 -10 | ||
E 1 | -1.868038×10 -12 | E 2 | 5.511305×10 -13 |
In performance function (3), select w
1=2, w
2=4, w
3=5, w
4=8, w
5=10 are oblique fire astigmatism weight factor, select w
6=1, w
7=2, w
8=3, w
9=10, w
10=14 is index of refraction error weight factor, selects w
11=0.2, w
12=0.5, w
13=0.5, w
14=0.8, w
15=1.2 are distortion weight factor, desired value t
1=t
2=...=t
14=t
15=0, by calculating, can be as oblique fire astigmatism and the index of refraction error curve diagram of Figure 1A for the optimization of existing aspherical focusing lens five visual fields, the distortion curve figure that Figure 1B optimizes for existing aspherical focusing lens five visual fields.
Wherein, among Figure 1A, abscissa axis is represented the size of index of refraction, and axis of ordinates is represented the size of field angle; Among Figure 1B figure, abscissa axis is represented the size that distorts, and axis of ordinates is represented the size of field angle.F among Figure 1A
T' be the index of refraction of imaging surface in the meridian field, F
S' be 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 Figure 1B is the size of distortion in each visual field, then:
By Figure 1A and Figure 1B, obviously can find out at place, 0.97 visual field has an extremely precipitous peak, is 24.433D by the oblique fire astigmatism that calculates herein, and the index of refraction error is 13.373D, and distortion is 6.23%, so effect is relatively poor.
When visual field of increase was optimized, oblique fire astigmatism, index of refraction error and distortion at place, 0.97 visual field still had a bigger value.
So aspherical focusing lens adopts five or six visual fields optimizations, all can not eliminate aberration preferably.
[summary of the invention]
In view of this, be necessary to design a kind of eyeglass, make this eyeglass be easy to make, and not only thin but also can effectively eliminate aberration.
A kind of aspherical focusing lens comprises first aspheric surface and second aspheric surface, and wherein the index of refraction of this aspherical focusing lens changes in the 1D scope, and first aspheric surface is fixed, and makes this aspherical focusing lens at least 7 visual fields, makes performance function
Desired value t
iBe zero, w wherein
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.
Compared with prior art, this aspherical focusing lens is because in index of refraction was changed to the 1D scope, first aspheric surface was fixed, and is optimized design at least 7 visual fields, so have the following advantages:
1. than changing with the eyeglass index of refraction, two aspheric surface designs need the aspherical focusing lens of change simultaneously, and aspherical focusing lens of the present invention is easy to make.
2. than being less than the aspherical focusing lens that 7 visual fields are optimized design, the oblique fire astigmatism of aspherical focusing lens of the present invention, index of refraction error and distortion are all less in 0 visual field to 1.0 field range.
[description of drawings]
Oblique fire astigmatism and index of refraction error curve diagram that Figure 1A optimizes for existing aspherical focusing lens five visual fields.
The distortion curve figure that Figure 1B optimizes for existing aspherical focusing lens five visual fields.
Fig. 2 is an aspherical focusing lens structural representation of the present invention.
Oblique fire astigmatism and index of refraction error curve diagram that Fig. 3 A optimizes for aspherical focusing lens of the present invention seven visual fields.
The distortion curve figure that Fig. 3 B optimizes for aspherical focusing lens of the present invention seven visual fields.
[embodiment]
As shown in Figure 2, be aspherical focusing lens structural representation of the present invention, this aspherical focusing lens comprises 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, optic diameter is DA.
Aspherical focusing lens of the present invention adopts damped least square method to come optimal design.In performance function (3), aspherical focusing lens design of the present invention is expressed as the process of aberration correction to desired value to be provided with 10 variable design parameters, is i.e. 10 design variable performance function.With x
1, x
2, x
3..., x
10The aspheric surface of representing first aspheric surface 1 is number P
1, B
1, C
1, D
1, E
1Be number P with the aspheric surface of second aspheric surface 2
2, B
2, C
2, D
2, E
2, P wherein
1, P
2Be conic constant value, B
1, C
1, D
1, E
1And B
2, C
2, D
2, E
2Be respectively first aspheric surface 1 and second aspheric surface, 2 high-order terms and be number.
By performance function (3) as can be known, optimizing item number has m, and aspherical focusing lens of the present invention can adopt m/3 item wherein to eliminate the oblique fire astigmatism when optimizing, and its time is according to the visual field size
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 (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 the aspheric surface of calculating first aspheric surface 1 is number P
1, B
1, C
1, D
1, E
1Be number P with the aspheric surface of 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 separating of damped least square method is (5)
X=(A
TA+pI)
-1A
Tf
0 (5)
Symbol in the formula can be used defined matrix:
A is the matrix of a m * n, wherein 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.
Aspherical focusing lens of the present invention is to adopt two aspheric surface designs, index of refraction at this aspherical focusing lens is changed in the 1D scope, first aspheric surface, 1 designs fix, and 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 these seven visual fields, 1.0 visual fields eliminate oblique fire astigmatism, index of refraction error and distortion.
If aspherical focusing lens of the present invention is to carry out the aspheric surface design in the eyeglass index of refraction is 12.00D to 12.75D or 14.00D to 14.75D.At first designing index of refraction is two aspheric surfaces of the aspherical focusing lens of 12.00D or 14.00D, when changing in the scope of index of refraction at 1D of this aspherical focusing lens, when promptly the index of refraction of this aspherical focusing lens is certain value of 12.00D to 12.75D or 14.00D to 14.75D, second aspheric surface 2 is carried out the aspheric surface design.Wherein, the aspheric surface design of second aspheric surface 2 is mainly two aspects, when the first was 12.00D to 12.75D or the some values of 14.00D to 14.75D when the index of refraction of this aspherical focusing lens, the design of the aspheric surface of second aspheric surface 2 made this aspherical focusing lens can reach this value; It two is to eliminate oblique fire astigmatism, index of refraction error and distortion in these seven visual fields of 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.
Because the aspheric surface of aspherical focusing lens of the present invention design, be at first to design two aspheric surfaces that the eyeglass index of refraction is 12.00D or 14.00D, when changing in the scope of index of refraction at 1D of this aspherical focusing lens, when promptly the index of refraction of this aspherical focusing lens is certain value of 12.25D, 12.50D, 12.75D or 14.25D, 14.50D, 14.75D, second aspheric surface 2 is carried out the aspheric surface design.
Therefore than change, need change the aspherical focusing lens of two aspheric surface designs simultaneously, make that aspherical focusing lens of the present invention is easy to make with the eyeglass index of refraction.
Aspherical focusing lens of the present invention 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 these seven visual fields, 1.0 visual fields are optimized, than being less than the aspherical focusing lens that 7 visual fields are optimized design, the oblique fire astigmatism of aspherical focusing lens of the present invention, index of refraction error and distortion are all less in visual field, 0 visual field to 1.0.
If aspherical focusing lens parameter of the present invention is as shown in table 2, when adopting 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 to optimize, the parameter of establishing this aspherical focusing lens is as shown in table 2.
Table 2
Eyeglass index of refraction F v=14.00D, optic diameter DA=32mm, center thickness t=9.2mm | |||||
First aspheric surface | Second aspheric surface | ||||
Radius of curvature R 1(cm) | 26.27803 | Radius of curvature R 1(cm) | 50.45961 | ||
The quadric surface constant P 1 | -3.961846 | The quadric surface constant P 2 | -3.228008 | ||
The first aspheric aspheric surface is number | B 1 | 1.989787×10 -5 | The second aspheric aspheric surface is number | 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 (3), 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 oblique fire astigmatism and the index of refraction error curve diagram optimized for aspherical focusing lens of the present invention seven visual fields as Fig. 3 A, the distortion curve figure that Fig. 3 B optimizes for aspherical focusing lens of the present invention seven visual fields.
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
T' be the index of refraction of imaging surface in the meridian field, F
S' be 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. 3 B is the size of distortion in each visual field, then:
By Fig. 3 A and Fig. 3 B, can find out that obviously the optimization effect of oblique fire astigmatism, the distortion of index of refraction sum of errors obviously is better than adopting the optimization effect of five visual fields.By calculating as can be known, in visual field, whole 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.
For further specifying aspherical focusing lens of the present invention in index of refraction is changed to the 1D scope, first aspheric surface 1 is fixing, and is optimized the superiority of design at least 7 visual fields, can describe by the table 3 and the design result of table 4.
Table 3 is a kind of aspheric surface design result of aspherical focusing lens, the index of refraction of this aspherical focusing lens is got 12.00D in variation range is 1D, 12.25D, 12.50D and four values of 12.75D, at first design two aspheric surfaces of the aspherical focusing lens of 12.00D, design 12.00D again, 12.25D, 12.50D or the aspherical focusing lens of 12.75D, fix first aspheric surface 1, optimize second aspheric surface 2, make the index of refraction of this aspherical focusing lens can be 12.00D wherein, 12.25D, 12.50D or the value of 12.75D, adopt 0.3 visual field in the design process, 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 are optimized, this design result makes the oblique fire astigmatism, it is all less when the distortion of index of refraction sum of errors is spent in maximum field of view angle u '=30.
Table 3
Aspheric surface positive lens density=1.25g/cm 3, diameter=32mm eyeglass index of refraction | |||||
Project | 12.00D | 12.25D | 12.50D | 12.75D | |
The first aspheric curvature radius R 1(cm) | 27.25581 | 27.25581 | 27.25581 | 27.25581 | |
The quadric surface constant P 1 | -4.335188 | -4.335188 | -4.335188 | -4.335188 | |
The first aspheric aspheric surface is number | B 1 | 1.748785×10 -5 | 1.748785×10 -5 | 1.748785×10 -5 | 1.748785×10 -5 |
C 1 | -8.839786×10 -8 | -8.839786×10 -8 | -8.839786×10 -8 | -8.839786×10 -8 | |
D 1 | -1.036805×10 -10 | -1.036805×10 -10 | -1.036805×10 -10 | -1.036805×10 -10 | |
E 1 | 7.419142×10 -14 | 7.419142×10 -14 | 7.419142×10 -14 | 7.419142×10 -14 | |
The second aspheric curvature radius R 2(cm) | 47.64221 | 48.63063 | 49.66094 | 50.73585 | |
The quadric surface constant P 2 | -3.523999 | -3.446832 | -3.373599 | -3.304074 | |
The second aspheric aspheric surface is number | B 2 | -2.379001×10 -5 | -2.430273×10 -5 | -2.476346×10 -5 | -2.51747×10 -5 |
C 2 | -1.311787×10 -7 | -1.268362×10 -7 | -1.227886×10 -7 | -1.190237×10 -7 | |
D 2 | 3.956243×10 -10 | 3.857511×10 -10 | 3.766512×10 -10 | 3.682946×10 -10 | |
E 2 | -4.849154×10 -13 | -4.776983×10 -13 | -4.712946×10 -13 | -4.656732×10 -13 | |
Center thickness (cm) | 8.5 | 8.5 | 8.5 | 8.5 | |
Oblique fire astigmatism (D) is in u '=30 ° | 0.0100 | 0.0096 | 0.0095 | 0.0094 | |
Refractive index error (D) is in u '=30 ° | -0.0109 | -0.0110 | -0.0112 | -0.0114 | |
Distortion (%) is in u '=30 ° | 0.8654 | 1.1561 | 1.4480 | 1.7403 |
Table 4 is the design result of 14.00D, 14.25D, 14.50D to 14.75D at index of refraction for a kind of aspherical focusing lens, the aspheric surface design concept of its design concept and table 3 is identical, and only the index of refraction of this aspherical focusing lens is got four values of 14.00D, 14.25D, 14.50D or 14.75D.
Table 4
Aspheric surface positive 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) | 26.27803 | 26.27803 | 26.27803 | 26.27803 | |
The quadric surface constant P 1 | -3.961846 | -3.961846 | -3.961846 | -3.961846 | |
First is aspheric | B 1 | 1.989787×10 -5 | 1.989787×10 -5 | 1.989787×10 -5 | 1.989787×10 -5 |
C 1 | -8.046623×10 -8 | -8.046623×10 -8 | -8.046623×10 -8 | -8.046623×10 -8 |
Aspheric surface is number | D 1 | -1.679019×10 -10 | -1.679019×10 -10 | -1.679019×10 -10 | -1.679019×10 -10 |
E 1 | 1.10465×10 -13 | 1.10465×10 -13 | 1.10465×10 -13 | 1.10465×10 -13 | |
The second aspheric curvature radius R 2(cm) | 50.45961 | 51.56976 | 52.72985 | 53.94334 | |
The quadric surface constant P 2 | -3.130257 | -3.083172 | -3.038703 | -2.996793 | |
The second aspheric aspheric surface is number | B 2 | -2.219438×10 -5 | -2.251372×10 -5 | -2.279043×10 -5 | -2.302616×10 -5 |
C 2 | -1.6121×10 -7 | -1.577234×10 -7 | -1.544997×10 -7 | -1.515303×10 -7 | |
D 2 | 5.025904×10 -10 | 4.94697×10 -10 | 4.875318×10 -10 | 4.810728×10 -9 | |
E 2 | -6.283488×10 -13 | -6.233038×10 -13 | -6.190522×10 -13 | -6.155703×10 -11 | |
Center thickness (cm) | 9.2 | 9.2 | 9.2 | 9.2 | |
Oblique fire astigmatism (D) is in u '=30 ° | 0.0145 | 0.0145 | 0.0147 | 0.0144 | |
Refractive index error (D) is in u '=30 ° | -0.0153 | -0.0156 | -0.0160 | -0.0167 | |
Distortion (%) is in u '=30 ° | 1.1493 | 1.4389 | 1.7290 | 2.0198 |
Can find out that by table 3 and table 4 index of refraction of aspherical focusing lens is in 12.00D to 12.75D and 14.00D to 14.75D, at maximum field of view angle u '=30 degree places, the oblique fire astigmatism is less than 0.0147D, the index of refraction error is less than 0.0167D, and distortion is less than 2.0198%, and these three kinds of aberrations are all less.
Be the aberration of explanation other field angle of 30 degree, can draw as table 5, shown in the table 6, table 7, be respectively the details of oblique fire astigmatism, index of refraction error and the distortion of 12.00D to 12.75D and 14.00D to 14.75D by calculating at the maximum field of view angle.
Table 5
Visual field ratio | Oblique fire astigmatism (D) eyeglass index of refraction | |||||||
12.00D | 12.25D | 12.50D | 12.75D | 14.00D | 14.25D | 14.50D | 14.75D | |
0.05 | -0.0023 | -0.0018 | -0.0013 | -0.0009 | -0.0055 | -0.0052 | -0.0049 | -0.0047 |
0.10 | -0.0078 | -0.0058 | -0.0040 | -0.0025 | -0.0192 | -0.0179 | -0.0169 | -0.0160 |
0.15 | -0.0130 | -0.0089 | -0.0053 | -0.0020 | -0.0338 | -0.0312 | -0.0291 | -0.0273 |
0.20 | -0.0145 | -0.0079 | -0.0020 | 0.0032 | -0.0413 | -0.0373 | -0.0340 | -0.0312 |
0.25 | -0.0104 | -0.0015 | 0.0065 | 0.0137 | -0.0369 | -0.0316 | -0.0271 | -0.0235 |
0.30 | -0.0023 | 0.0086 | 0.0184 | 0.0272 | -0.0214 | -0.0150 | -0.0097 | -0.0053 |
0.35 | 0.0060 | 0.0182 | 0.0292 | 0.0392 | -0.0013 | 0.0057 | 0.0118 | 0.0167 |
0.40 | 0.0095 | 0.0224 | 0.0341 | 0.0448 | 0.0138 | 0.0214 | 0.0279 | 0.0334 |
0.45 | 0.0054 | 0.0182 | 0.0302 | 0.0412 | 0.0163 | 0.0243 | 0.0315 | 0.0377 |
0.50 | -0.0056 | 0.0067 | 0.0184 | 0.0295 | 0.0045 | 0.0130 | 0.0209 | 0.0282 |
0.55 | -0.0190 | -0.0073 | 0.0041 | 0.0151 | -0.0161 | -0.0068 | 0.0021 | 0.0108 |
0.60 | -0.0274 | -0.0163 | -0.0053 | 0.0057 | -0.0341 | -0.0238 | -0.0134 | -0.0029 |
0.65 | -0.0246 | -0.0140 | -0.0031 | 0.0080 | -0.0377 | -0.0259 | -0.0138 | -0.0012 |
0.70 | -0.0092 | 0.0018 | 0.0120 | 0.0233 | -0.0205 | -0.0074 | 0.0064 | 0.0207 |
0.75 | 0.0127 | 0.0225 | 0.0332 | 0.0444 | 0.0117 | 0.0262 | 0.0391 | 0.0545 |
0.80 | 0.0260 | 0.0350 | 0.0443 | 0.0543 | 0.0369 | 0.0491 | 0.0621 | 0.0755 |
0.85 | 0.0141 | 0.0208 | 0.0278 | 0.0349 | 0.0265 | 0.0344 | 0.0426 | 0.0509 |
0.90 | -0.0213 | -0.0164 | -0.0117 | -0.0071 | -0.0266 | -0.0235 | -0.0207 | -0.0182 |
0.95 | -0.0150 | -0.0060 | 0.0032 | 0.0125 | -0.0178 | -0.0079 | 0.0022 | 0.0121 |
1.00 | 0.0100 | 0.0096 | 0.0095 | 0.0094 | 0.0145 | 0.0145 | 0.0147 | 0.0144 |
Table 6
Visual field ratio | Index of refraction error (D) eyeglass index of refraction | |||||||
12.00D | 12.25D | 12.50D | 12.75D | 14.00D | 14.25D | 14.50D | 14.75D | |
0.05 | -0.0042 | -0.0037 | -0.0032 | -0.0028 | -0.0076 | -0.0073 | -0.0070 | -0.0068 |
0.10 | -0.0150 | -0.0131 | -0.0114 | -0.0099 | -0.0276 | -0.0264 | -0.0254 | -0.0246 |
0.15 | -0.0281 | -0.0241 | -0.0206 | -0.0174 | -0.0524 | -0.0500 | -0.0479 | -0.0462 |
0.20 | -0.0385 | -0.0320 | 0.0262 | -0.0211 | -0.0729 | -0.0690 | -0.0657 | -0.0631 |
0.25 | -0.0420 | -0.0329 | -0.0248 | -0.0177 | -0.0815 | -0.0762 | -0.0718 | -0.0684 |
0.30 | -0.0371 | -0.0257 | -0.0156 | -0.0066 | -0.0752 | -0.0687 | -0.0634 | -0.0592 |
0.35 | -0.0254 | -0.0122 | -0.0004 | 0.0099 | -0.0562 | -0.0488 | -0.0428 | -0.0382 |
0.40 | -0.0107 | 0.0037 | 0.0165 | 0.0280 | -0.0311 | -0.0232 | -0.0168 | -0.0118 |
0.45 | 0.0025 | 0.0173 | 0.0305 | 0.0422 | -0.0082 | 0.0000 | 0.0066 | 0.0118 |
0.50 | 0.0107 | 0.0252 | 0.0383 | 0.0499 | 0.0061 | 0.0143 | 0.0211 | 0.0265 |
0.55 | 0.0126 | 0.0263 | 0.0386 | 0.0496 | 0.0093 | 0.0174 | 0.0242 | 0.0298 |
0.60 | 0.0097 | 0.0218 | 0.0329 | 0.0428 | 0.0033 | 0.0111 | 0.0179 | 0.0237 |
0.65 | 0.0045 | 0.0147 | 0.0240 | 0.0324 | -0.0063 | 0.0010 | 0.0075 | 0.0133 |
0.70 | 0.0004 | 0.0078 | 0.0147 | 0.0210 | -0.0132 | -0.0070 | -0.0013 | 0.0040 |
0.75 | -0.0013 | 0.0027 | 0.0064 | 0.0099 | -0.0134 | -0.0086 | -0.0058 | -0.0020 |
0.80 | -0.0012 | -0.0015 | -0.0021 | -0.0029 | -0.0088 | -0.0084 | -0.0081 | -0.0078 |
0.85 | -0.0011 | -0.0068 | -0.0126 | -0.0185 | -0.0047 | -0.0100 | -0.0153 | -0.0208 |
0.90 | 0.0016 | -0.0083 | -0.0183 | -0.0285 | -0.0026 | -0.0132 | -0.0240 | -0.0351 |
0.95 | 0.0254 | 0.0182 | 0.0111 | 0.0041 | 0.0314 | 0.0247 | 0.0182 | 0.0116 |
1.00 | -0.0109 | -0.0111 | -0.0112 | -0.0114 | -0.0153 | -0.0156 | -0.0160 | -0.0167 |
Table 7
Visual field ratio | Distortion (%) eyeglass index of refraction | |||||||
12.00D | 12.25D | 12.50D | 12.75D | 14.00D | 14.25D | 14.50D | 14.75D | |
0.05 | -0.0127 | -0.0115 | -0.0104 | -0.0094 | -0.0210 | -0.0202 | -0.0194 | -0.0188 |
0.10 | -0.0472 | -0.0424 | -0.0379 | -0.0338 | -0.0774 | -0.0743 | -0.0714 | -0.0690 |
0.15 | -0.0930 | -0.0825 | -0.0727 | -0.0637 | -0.1525 | -0.1454 | -0.1392 | -0.1338 |
0.20 | -0.1368 | -0.1187 | -0.1019 | -0.0863 | -0.2235 | -0.2112 | -0.2003 | -0.1908 |
0.25 | -0.1661 | -01390 | -0.1138 | -0.0903 | -0.2691 | -0.2504 | -0.2338 | -0.2191 |
0.30 | -0.1735 | -0.1364 | -0.1017 | -0.0693 | -0.2759 | -0.2498 | -0.2264 | -0.2056 |
0.35 | -0.1591 | -0.1114 | -0.0666 | -0.0247 | -0.2425 | -0.2082 | -0.1771 | -0.1493 |
0.40 | -0.1313 | -0.0728 | -0.0176 | 0.0342 | -0.1809 | -0.1377 | -0.0983 | -0.0626 |
0.45 | -0.1046 | -0.0355 | 0.0299 | 0.0916 | -0.1142 | -0.0616 | -0.0132 | 0.0310 |
0.50 | -0.0965 | -0.0175 | 0.0577 | 0.1290 | -0.0705 | -0.0085 | 0.0492 | 0.1024 |
0.55 | -0.1227 | -0.0345 | 0.0497 | 0.1300 | -0.0759 | -0.0046 | 0.0624 | 0.1249 |
0.60 | -0.1916 | -0.0955 | -0.0032 | 0.0853 | -0.1458 | -0.0655 | 0.0106 | 0.0824 |
0.65 | -0.3003 | -0.1975 | -0.0982 | -0.0024 | -0.2777 | -0.1890 | -0.1042 | -0.0234 |
0.70 | -0.4310 | -0.3227 | -0.2175 | -0.1154 | -0.4463 | -0.3500 | -0.2570 | -0.1676 |
0.75 | -0.5489 | -0.4361 | -0.3257 | -0.2178 | -0.6019 | -0.4978 | -0.3986 | -0.3006 |
0.80 | -0.6023 | -0.4849 | -0.3694 | -0.2556 | -0.6738 | -0.5634 | -0.4551 | -0.3490 |
0.85 | -0.5259 | -0.4014 | -0.2780 | -0.1559 | -0.5736 | -0.4544 | -0.3367 | -0.2205 |
0.90 | -0.2507 | -0.1101 | 0.0299 | 0.1693 | -0.2168 | -0.0809 | 0.0542 | 0.1881 |
0.95 | 0.2603 | 0.4427 | 0.6252 | 0.8077 | 0.4327 | 0.6113 | 0.7894 | 0.9669 |
1.00 | 0.8654 | 1.1561 | 1.4480 | 1.7403 | -1.1493 | 1.4389 | 1.7290 | 2.0198 |
From table 5, table 6, table 7 as can be known, 0 the degree to 30 the degree whole field range in the oblique fire astigmatism less than 0.0755D, the index of refraction error is less than 0.0815D, distortion is less than 2.0198%, and this aberration of three kinds is all less, so aspherical focusing 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 focusing lens of the present invention can be realized being easy to making, and is not only thin but also effectively eliminate the purpose of aberration.Only, the above only is preferred embodiment of the present invention, 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 (6)
1. an aspherical focusing lens comprises first aspheric surface and second aspheric surface, it is characterized in that: the index of refraction of this aspherical focusing lens changes in the 1D scope, and first aspheric surface is fixed, and makes this aspherical focusing lens at least 7 visual fields, makes performance function
Desired value t
iBe zero, w wherein
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.
2. aspherical focusing lens as claimed in claim 1 is characterized in that: this performance function has 10 Variable Designing Of parameters.
3. aspherical focusing lens as claimed in claim 2 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 first aspheric surface and the second aspheric conic constant value, B
1, C
1, D
1, E
1Be that the first aspheric surface high-order term is number, B
2, C
2, D
2, E
2Be that the second aspheric surface high-order term is number.
4. as claim 2 or 3 described aspherical focusing lens, it is characterized in that: these 10 Variable Designing Of parameters are to calculate the performance function gained by damped least square method.
5. aspherical focusing lens as claimed in claim 1 is characterized in that: these 7 visual fields can be respectively 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.
6. aspherical focusing lens as claimed in claim 5 is characterized in that: 1.0 visual fields are that the field angle at this aspherical focusing lens is the positions of 30 degree.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CNB200510034105XA CN100426037C (en) | 2005-04-07 | 2005-04-07 | Aspherical focusing lens |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CNB200510034105XA CN100426037C (en) | 2005-04-07 | 2005-04-07 | Aspherical focusing lens |
Publications (2)
Publication Number | Publication Date |
---|---|
CN1844967A true CN1844967A (en) | 2006-10-11 |
CN100426037C CN100426037C (en) | 2008-10-15 |
Family
ID=37063909
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CNB200510034105XA Expired - Fee Related CN100426037C (en) | 2005-04-07 | 2005-04-07 | Aspherical focusing lens |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN100426037C (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN108333748A (en) * | 2018-02-24 | 2018-07-27 | 京东方科技集团股份有限公司 | A kind of the lens optimization method and device of virtual reality device |
US10585309B2 (en) | 2016-11-23 | 2020-03-10 | Shenzhen Mingzhi Ultra Precision Technology Co., Ltd. | Ellipsoid wide angle backlight lens |
Family Cites Families (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH0634877A (en) * | 1992-07-14 | 1994-02-10 | Konica Corp | Photographing lens, photographing lens system, and camera |
JPH07261088A (en) * | 1994-03-18 | 1995-10-13 | Olympus Optical Co Ltd | Homocentric optical system |
CN2257609Y (en) * | 1995-03-31 | 1997-07-09 | 吴祥照 | Non-spherical lens |
KR100506565B1 (en) * | 2000-11-16 | 2005-08-10 | 닛뽕빅터 가부시키가이샤 | Objective lens for an optical disk |
-
2005
- 2005-04-07 CN CNB200510034105XA patent/CN100426037C/en not_active Expired - Fee Related
Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US10585309B2 (en) | 2016-11-23 | 2020-03-10 | Shenzhen Mingzhi Ultra Precision Technology Co., Ltd. | Ellipsoid wide angle backlight lens |
CN108333748A (en) * | 2018-02-24 | 2018-07-27 | 京东方科技集团股份有限公司 | A kind of the lens optimization method and device of virtual reality device |
WO2019161699A1 (en) * | 2018-02-24 | 2019-08-29 | 京东方科技集团股份有限公司 | Method and apparatus for optimizing lens of virtual reality device, and computer readable storage medium |
CN108333748B (en) * | 2018-02-24 | 2021-01-26 | 京东方科技集团股份有限公司 | Lens optimization method and device of virtual reality equipment |
US11536957B2 (en) | 2018-02-24 | 2022-12-27 | Beijing Boe Optoelectronics Technology Co., Ltd. | Method and apparatus for optimizing a lens of a virtual reality device, and computer readable storage medium |
Also Published As
Publication number | Publication date |
---|---|
CN100426037C (en) | 2008-10-15 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN1132042C (en) | Method for design of multifocal optical elements | |
CN101029958A (en) | Optical device | |
CN1285942C (en) | Lens device for projection, and back projecting display using such lens device | |
CN1892278A (en) | Imaging lens | |
CN1068435C (en) | Zoom lens | |
JP2004061938A (en) | Imaging lens | |
US11536957B2 (en) | Method and apparatus for optimizing a lens of a virtual reality device, and computer readable storage medium | |
JPS59149312A (en) | Photographic lens of high aperture ratio | |
CN1866077A (en) | Fourier transform optical system and volume holographic storage Fourier transform optical system | |
CN1254099A (en) | Objective of endoscope | |
CN1841113A (en) | Aspherical lens | |
CN1854787A (en) | Method for designing non-spherical lens | |
CN1844967A (en) | Aspherical focusing lens | |
CN2763823Y (en) | Composite lens system | |
CN1201169C (en) | Projection lens system | |
CN1945370A (en) | Thin imaging lens group | |
JPH10311946A (en) | Triplet lens | |
US20060001830A1 (en) | Method for designing aspheric spectacle lens | |
WO2010079549A1 (en) | Image pickup lens system | |
CN1700048A (en) | Projection lens apparatus and rear projection type image display apparatus used the same | |
CN107728289A (en) | A kind of high pixel camera lens | |
CN210376860U (en) | Immersion microscope objective | |
CN1945373A (en) | Zooming projection lens | |
CN110673306A (en) | Small-size full high definition short-focus projection lens | |
CN115327745B (en) | High-flux flat-field apochromatic objective lens |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
C06 | Publication | ||
PB01 | Publication | ||
C10 | Entry into substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
C14 | Grant of patent or utility model | ||
GR01 | Patent grant | ||
CF01 | Termination of patent right due to non-payment of annual fee | ||
CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20081015 Termination date: 20160407 |