CN107632412B - A kind of ophthalmic progressive additional lens and preparation method thereof of center of curvature optimization - Google Patents
A kind of ophthalmic progressive additional lens and preparation method thereof of center of curvature optimization Download PDFInfo
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Abstract
The invention discloses a kind of ophthalmic progressive additional lens and preparation method thereof of center of curvature optimization.By establishing center of curvature y-coordinateTwo kinds of majorized functions to ophthalmic progressive additional lens surface rise expression formula mean curvature center in the prior artInIt optimizes, the lens surface rise after being optimized, then carries out the processing of eyeglass.The comparing result of lens surface rise optimization front and back shows that two majorized functions provided by the invention can be obviously improved the optical property of ophthalmic progressive additional lens, improves the wear comfort of lens wearer.
Description
Technical field
The present invention relates to a kind of ophthalmic progressive additional lens, in particular to a kind of progressive additional of center of curvature optimization
Eye lens and preparation method thereof.
Background technique
Ophthalmic progressive additional lens can meet simultaneously view far with regard the needs of close, in turn avoid double light microscopics etc. view far with
The defects of being broken depending on vision when nearly conversion.Referring to attached drawing 1, ophthalmic progressive additional lens surface is divided into the area Yuan Yong 1, gradual change channel
(or intermediate transition zone) area 2, Jin Yong (read area) 3 and spread area 4；In Fig. 1, A is the area Yuan Yong reference point, and B is the area Jin Yong ginseng
Examination point；The area Yuan Yong, the area Jin Yong and gradual change channel are referred to as effective visible sensation area.
Since the pupil of human eye is smaller, diameter only has 3 to 4 millimeters, and human eye and ophthalmic progressive additional lens constitute system
Aperture it is small, visual field is big, and spherical aberration and coma is smaller on mutually influencing, can not usually consider, and astigmatism be human eye is influenced it is maximum
Aberration, directly affect sharpness of vision, bring discomfort to the wearer of ophthalmic progressive additional lens.Therefore, in progressive multi-focal
Primary concern is that focal power reaches requirement and reduces unnecessary astigmatism, wherein reducing need not in the optimization design of point eye lens
Wanting astigmatism is the maximum difficult point in ophthalmic progressive additional lens design.
Before the present invention makes, United States Patent (USP) (US4861153) and Chinese invention patent (CN101661167A) are provided
Ophthalmic progressive additional lens design method are as follows: use cartesian coordinate system, origin is in center of lens, positive direction of the y-axis water
It puts down to the right, straight down, z-axis positive direction is directed toward reader perpendicular to paper to positive direction of the x-axis.The area Yuan Yong reference point and close is determined first
It is distributed with the focal power of area's reference point, then the curvature of meridian by determining the connection area Yuan Yong and the area Jin Yong, in conjunction with continuously distributed
Contour line u (x, y) determine the radius of curvature R (x, y) throughout entire eyeglass, and then by the radius of curvature value R (x, y) of each point
The center of curvature (ξ, η, ζ) (wherein η=0) of each point on eyeglass progressive additional surface is calculated, finally according to rise formula
Calculate progressive multi-focus lens rise distribution z (x, y).
In the prior art, Chinese invention patent (CN101661167A) mainly for radius of curvature R (x, y) on meridian into
Row optimization design is to reduce unnecessary astigmatism.Chinese invention patent (CN103246080A) is carried out mainly for contour line u (x, y)
Optimization design is to reduce unnecessary astigmatism.The center of curvature of each point is to ophthalmic progressive additional lens on progressive additional surface
Astigmatism also has a larger impact, in above-mentioned technical proposal, although the x coordinate ξ and z coordinate ζ to the center of curvature are calculated,
It is to set zero for the y-coordinate η pressure of the center of curvature, is unfavorable for reducing unnecessary astigmatism.
Summary of the invention
The present invention provides a kind of curvature for deficiency present in the design of the existing ophthalmic progressive additional lens center of curvature
The ophthalmic progressive additional lens and preparation method thereof of center optimization, effectively improve the optical of ophthalmic progressive additional lens
Energy.
Realize that the technical solution of the object of the invention is to provide a kind of ophthalmic progressive additional lens of center of curvature optimization
Preparation method, first obtains the surface rise of initial lens, and the center of curvature coordinate of initial lens is (ξ, η, ζ), lens surface
Radius of curvature be R=R (x, y), the x coordinate of the center of curvature is ξ=ξ (x, y), and y-coordinate is η=0, z coordinate be ζ=ζ (x,
Y), the optimization and processing of following two method are carried out then.
The step of method one, is as follows:
(1) to the majorized function table of the y-coordinate η in the center of curvature coordinate (ξ, η, ζ) of initial lens (I) as follows
It is optimized up to formula:
Wherein, sgn () is sign function；B is location parameter, and the value range of b is 0.4~1.2；κ is width parameter, κ
Value range be 0.6~1.2；For the bore of eyeglass；Optimized coefficients a1And a2(II) Nonlinear System of Equations meter as follows
It obtains:
Wherein, J1(a1,a2)=∫ ∫ F(1)Dxdy, F(1)For square of initial lens surface principal curvatures difference, F(1)=(k1-k2)2,
And (k1-k2)2=g-6[r(1+q2)-2pqs+t(1+q2)]2-4g-4(rt-s2),
Wherein,
(2) as follows (III) calculate eyeglass surface rise:
(3) the surface rise machining lens obtained with step (2) obtain a kind of ophthalmic progressive additional of center of curvature optimization
Use eyeglass.
The step of method two, is as follows:
(1) to the majorized function of the y-coordinate η in the center of curvature coordinate (ξ, η, ζ) of initial lens (IV) as follows
Expression formula optimizes:
In formula, R=R (x, y) is the surface curvature radius of initial lens；Optimized coefficients c1And c2(V) counts as follows
It obtains:
In formula, α is Dynamic gene, and value range is 0.2~0.8；c10And c20The respectively non-linear side of following formula (VI)
The root of journey group:
In formula, J2(c1,c2)=∫ ∫ F(2)Dxdy, F(2)For square of initial lens surface principal curvatures difference, F(2)=(k1-k2)2,
And (k1-k2)2=g-6[r(1+q2)-2pqs+t(1+q2)]2-4g-4(rt-s2),
Wherein,
(2) as follows (VII) calculate eyeglass surface rise:
(3) the surface rise machining lens obtained with step (2) obtain a kind of ophthalmic progressive additional of center of curvature optimization
Use eyeglass.
Technical solution of the present invention further includes the progressive more of the center of curvature optimization respectively obtained by above two preparation method
Focus eye lens.
Song on the basis of present invention ophthalmic progressive additional lens disclosed in the prior art, to obtained initial lens
Rate center optimizes, and constructs the majorized function of the y-coordinate η of two kinds of centers of curvature, and by ophthalmically acceptable to progressive additional
The method that lens surface principal curvatures difference integrated square function seeks extreme value, obtains the optimized coefficients in majorized function, to process
To the ophthalmic progressive additional lens advanced optimized, the optical property of ophthalmic progressive additional lens can effectively improve, improve
The wear comfort of lens wearer.
Detailed description of the invention
Fig. 1 is the different function area schematic of ophthalmic progressive additional lens；
Fig. 2 is that the embodiment of the present invention is equivalent by the focal power and astigmatism of the progressive multi-focus lens of prior art initial designs
Line chart；
Fig. 3 is the majorized function three dimensional network figure of 1 technical solution mean curvature center y-coordinate of the embodiment of the present invention；
Fig. 4 is the focal power and astigmatism isopleth by progressive multi-focus lens after the optimization of 1 technical solution of the embodiment of the present invention
Figure；
Fig. 5 is the majorized function three dimensional network figure of 2 technical solution mean curvature center y-coordinate of the embodiment of the present invention；
Fig. 6 is the focal power and astigmatism isopleth by progressive multi-focus lens after the optimization of 2 technical solution of the embodiment of the present invention
Figure.
Specific embodiment
Referring to Fig. 1, ophthalmic progressive additional lens surface is divided into the area Yuan Yong 1, the area Jin Yong 3, gradual change channel 2 and spread area 4.
The area Yuan Yong is located at the broad area of ophthalmic progressive additional lens top half, and there is correction to regard remote ability, provide clear, broad
The visual field；The area Jin Yong, which is located at, regards remote reference point central lower about 10~18mm, and for observing nearly object, optical clarity range is smaller；
Gradual change channel is the transitional region for connecting the area Yuan Yong and the area Jin Yong, for observing moderate distance object and progressive lenses difference
It is general relatively narrow in the main feature region of double light microscopics.The area Yuan Yong, the area Jin Yong and gradual change channel are referred to as effective visible sensation area；It is other
Region is spread area, it is impossible to be used in observation.
In cartesian coordinate system, origin in center of lens, positive direction of the y-axis horizontally to the right, positive direction of the x-axis straight down, z
Axis positive direction is directed toward reader perpendicular to paper.Length unit is all mm.A is that remote reference point is regarded on eyeglass, and B is the nearly ginseng of view on eyeglass
The line of examination point, A point to B point is downward along x-axis, referred to as meridian, length h.A point between center of lens point O away from
From for L.
The design method of ophthalmic progressive additional lens in the prior art CN101661167A, CN103246080A are as follows:
A kind of isopleth cluster u (x, y), the referred to as contour line of ophthalmic progressive additional lens are designed on x/y plane.It is every in contour line
One line has u (x, a y) value.Lens surface radius of curvature R is the function of u, as shown in formula (1):
Wherein, RdThe radius of curvature at reference point A, R are far used for lens surfacebThe song at reference point B is closely used for lens surface
Rate radius, m are at point AThe minimum order of first non-zero derivative, l are above formula at point BFirst non-zero derivative
Minimum order.Lens powers are shown in following formula (2):
Wherein n0For the refractive index of eyeglass.The unit of focal power is diopter (m-1)。
Each radius of curvature R corresponds to a spherical surface, and a series of enveloping surface of this spherical surface is exactly progressive additional lens
Surface rise.It can be indicated by formula (3) are as follows:
Z (x, y)=ζ-[R2-(x-ξ)2-(y-η)2]1/2 (3)
Wherein, R is progressive multi-focus lens surface curvature radius, and (ξ, η, ζ) is the center of curvature, referring to formula (4):
Wherein,
According to Differential Geometry rudimentary knowledge, the principal curvatures k of each point on eyeglass1And k2Meet the quadratic equation with one unknown of k, as a result
Such as formula (5):
g4k2+g[2pqs-(1+p2)t-(1+q2)r]k+(rt-s2)=0 (5)
Wherein:
Formula (6) can be obtained according to the relationship of formula (5) root and coefficient:
(k1-k2)2=g-6[r(1+q2)-2pqs+t(1+q2)]2-4g-4(rt-s2) (6)
The average focal power of each point is by shown in formula (7) on eyeglass:
Astigmatism is by shown in formula (8):
Φast=(n0-1)|k1-k2|×103 (8)
The unit of average focal power and astigmatism is diopter, and symbol is (m-1)。
For the prior art in formula (4), center of curvature y-coordinate η is always zero.
The technical scheme is that establishing the majorized function η (x, y) of y-coordinate η in the center of curvature (ξ, η, ζ), substitute into public
Formula (3) optimized after ophthalmic progressive additional lens surface rise.
Technical solution of the present invention includes two kinds of majorized functions, is described below respectively:
1. majorized function (1)
It is high astigmatism areas because ophthalmic progressive additional lens surface needs optimize, usual high spread area is only distributed in mirror
Two specific regions on piece surface, therefore majorized function should have certain nonzero value in the region, be in other regions
Zero, in order to avoid unnecessary astigmatism, it is desirable that the variation from nonzero value to zero must smooth gradual change.
In the technical solution of the present invention, using the optimization of probability function and triangle cosine function building center of curvature y-coordinate
Shown in function such as formula (9):
Wherein, sgn () is sign function；B is location parameter, the distributing position of control function；κ is width parameter, control
The dispersion of distribution of function；For the bore of progressive multi-focus lens；a1And a2For undetermined coefficient.According to initial designs progressive multi-focal
B is arranged in the x coordinate value of point eye lens maximum astigmatism distribution position, and value range is 0.4 to 1.2；According to the width of high spread area
κ is arranged in angle value, and value range is 0.6 to 1.2.
Suitable coefficient a in order to obtain1、a2, formula (9) are substituted into formula (3) and are obtained, z is to include R, ζ, ξ, x, y, a1、a2,
There are also the b of setting and κ, as formula (10):
Wherein, R=R (x, y), ξ=ξ (x, y) and ζ=ζ (x, y) are respectively the progressive additional of prior art initial designs
The radius of curvature on eye lens surface, the x coordinate of the center of curvature and z coordinate.
Partial derivative is asked to obtain the expression (change in corresponding expression formula of following 5 partial derivatives z in formula (10)
Amount) such as formula (11), (12), (13), (14) and (15) are shown respectively:
It is formula (16) by the expression formula that formula (11) to (15) substitution formula (6) obtains principal curvatures difference square:
F(1)=(k1-k2)2 (16)
F(1)In (k1-k2)2Expression formula is formula (6), wherein p, q, r, and s, t are to seek local derviation to the z (x, y) in formula (10)
Obtained formula (11) to (15) formula, i.e.,
Wherein comprising ζ, R, ξ, x、y、a1、a2, b and κ, wherein removing a1、a2, b and κ
Outside, surplus can be obtained according in the specific calculating of above-mentioned ophthalmic progressive additional lens design formula (1) to formula (6)
It arrives；B and κ is preset adjusting parameter, can position according to the eyeglass spread area of prior art initial designs and width tune
It is whole；a1,a2For undetermined coefficient.
Progressive multi-focus lens principal curvatures difference integrated square functional is formula (17):
J1(a1,a2)=∫ ∫ F(1)dxdy (17)
The integral domain of the functional is entire ophthalmic progressive additional lens.
Because of the focal power consecutive variations of ophthalmic progressive additional lens, the integrated square J of principal curvatures difference1(a1,a2) must have
Minimum value.According to variation principle, J1(a1,a2) when taking extreme value, then there is a1、a2Binary nonlinear equation group such as formula (18):
When solving above-mentioned Nonlinear System of Equations, genetic algorithm can be used or above-mentioned Nonlinear System of Equations is rule of thumb set
Initial value, then with Levenberg-Marquardt algorithm obtain precision be 10-6A1And a2Numerical solution.
The a that will be obtained1、a2Value substitute into formula (9) and obtain majorized function η (x, y), η (x, y) substitute into formula (3) obtain it is excellent
The surface rise of ophthalmic progressive additional lens after change obtains a kind of ophthalmically acceptable mirror of progressive additional after processing by the surface rise
Piece.
2. majorized function (2)
Technical solution of the present invention proposes another majorized function of the center of curvature y-coordinate of ophthalmic progressive additional lens such as
Shown in formula (19):
Wherein, R is the ophthalmic progressive additional lens surface curvature radius according to prior art initial designs, c1And c2For
Undetermined coefficient.
Suitable c in order to obtain1And c2, formula (19) are substituted into formula (3), obtain formula (20):
Wherein, R=R (x, y), ξ=ξ (x, y) and ζ=ζ (x, y) are respectively the progressive additional of prior art initial designs
The radius of curvature on eye lens surface, the x coordinate of the center of curvature and z coordinate, c1And c2For undetermined coefficient.
Partial derivative is asked to obtain the expression (change in corresponding expression formula of following 5 partial derivatives z in formula (20)
Amount) be respectively following formula (21), (22), (23), (24) and (25):
Formula (21) to (25) substitution formula (6) is obtained into the expression formula such as formula (26) of principal curvatures difference square:
F(2)=(k1-k2)2 (26)
F(2)In (k1-k2)2Expression formula is formula (6), and p, q, r in formula, s, t are to seek local derviation to the z (x, y) in formula (20)
Obtained formula (21) to (25) formula, i.e., Wherein comprising ζ, R, ξ, x、y、c1And c2, wherein removing c1And c2Outside, surplus can be according to above-mentioned ophthalmic progressive additional lens design formula
(1) it is obtained into the specific calculating of (6).
Progressive multi-focus lens principal curvatures difference integrated square functional is formula (27):
J2(c1,c2)=∫ ∫ F(2)dxdy (27)
The integral domain of the functional is entire ophthalmic progressive additional lens.
Because of ophthalmic progressive additional lens focal power consecutive variations, the integrated square J of principal curvatures difference2(c1,c2) must have most
Small value.According to variation principle, J2(c1,c2) when taking extreme value, then there is c1、c2Binary nonlinear equation group see formula (28):
When solving above-mentioned Nonlinear System of Equations, genetic algorithm can be used or above-mentioned Nonlinear System of Equations is rule of thumb set
Initial value, then with Levenberg-Marquardt algorithm obtain precision be 10-6Numerical solution.Current main-stream PC solves
2 to 5 minutes general used times of process, the root c of obtained non-linear two element equations formula (28)10、c20Value.
Since the majorized function influences whether the lesser region of astigmatism on ophthalmic progressive additional lens, in order to not influence small
A Dynamic gene α is added in the optical property of astigmatism areas, even for shown in formula (29):
The value range of α is 0.2 to 0.8.The c that will be obtained1And c2Value substitute into formula (19) obtain majorized function η (x,
Y), η (x, y) substitutes into the surface rise of the ophthalmic progressive additional lens after formula (3) are optimized, and pressing should.Surface rise adds
Work eyeglass obtains a kind of ophthalmic progressive additional lens.
Technical solution of the present invention is further described with reference to the accompanying drawings and embodiments.
Embodiment 1
In the present embodiment, luminosity number is added to be the inner progressive multiple-focus of 2 diopters according to Demand Design one with mirror person
Eyeglass, lens materials refractive index 1.532, optic diameterThe designed area inner surface Yuan Yong focal power ΦPA
For -4 diopters；The area Jin Yong focal power ΦPBFor -2 diopters.
By profile line design method disclosed in Chinese invention CN103246080A, obtains contour line and be distributed u (x, y), h, L,
M, the value of l is taken as 30,12,9 and 6 respectively, and grid point step size is 3mm.By u (x, y) substitute into formula (1) and formula (4) obtain R,
ξ, η, ζ, wherein η=0, obtains the initial rise of ophthalmic progressive additional lens for R, ξ, η, ζ substitution (3) formula.
Single order and second-order partial differential coefficient is asked to obtain z using central difference method: It substitutes into and solves linear equation in two unknowns
(5) k is obtained1And k2, substituted into formula (7) and formula (8) be calculated the initial focal power of ophthalmic progressive additional lens and dissipate
Light distribution figure, result are as shown in Fig. 2.The area the Yuan Yong focal power of initial designs eyeglass is -4 diopters, and the area Yuan Yong clearly regards
Feel that range (range of the astigmatism less than 0.25 diopter) is larger, about 140 ° of the upward subtended angle of Yuan Yongqu optical clarity range, glasses wearer
There is the openr visual field when depending on remote, but the local astigmatism of y=± 10mm is up to 2.39 diopters on eyeglass.
Majorized function (1) is used in the present embodiment, i.e. formula (9).B=0.8084 and κ=0.8671 are rule of thumb taken, is adopted
Single order and second-order partial differential coefficient is asked to obtain ζ, R, ξ of initial designs respectively with central difference method Above-mentioned amount substitution formula (16) is obtained into the expression formula F of principal curvatures difference square(1), by F(1)It substitutes into formula (18), obtains
To about a1、a2Binary nonlinear equation group.A is set1、a2Initial value is zero, with Levenberg-Marquardt algorithm
Solve a1=0.0106, a2=-0.0031.
By a1、a2, b and κ value substitute into formula (9) and obtain majorized function η (x, y).The distribution of majorized function η (x, y) is for example attached
Shown in Fig. 3, as can be seen from the figure: the distributing position and initial designs ophthalmic progressive additional of the nonzero value of majorized function η (x, y)
Be overlapped with the high spread area of eyeglass, it is almost nil in the value of other optimization of region function ηs (x, y), ensure that low spread area not by
The influence of majorized function.
The surface rise of ophthalmic progressive additional lens after η (x, y) substitution formula (3) is optimized.After optimization gradually
It is as shown in Fig. 4 into the initial focal power of multifocal ophthalmic lens and astigmatism distribution.
In the present embodiment, optimization front and back ophthalmic progressive additional lens optical performance parameter is as shown in table 1.Initial designs
The area the Yuan Yong focal power of ophthalmic progressive additional lens is -4 diopters, and additional optical focal power is 2 diopters.The clear vision in the area Yuan Yong
Range (range of the astigmatism less than 0.25 diopter) is larger, in the position of x=-10mm, width of the astigmatism less than 0.25 diopter
Up to 54mm, and the local astigmatism of x=10mm on eyeglass, y=± 10mm, up to 2.39 diopters, biggish astigmatism seriously affects progressive
The wear comfort of multifocal ophthalmic lens user.
The focal power in the area ophthalmic progressive additional lens Yuan Yong and the area Jin Yong has almost no change after optimization, in x=-10mm
Position, astigmatism reaches 40mm, smaller than initial designs width 14mm less than the width of 0.25 diopter；Maximum astigmatism reduces
0.16 diopter, about reduces 6.7%；And big spread area (region that astigmatism is more than or equal to 2 diopters) arrives central axes most
13mm is closely increased to by original 7mm.Compared with initial designs, far slightly reduced with sector width, but the mirror after optimizing
Not only maximum astigmatism effectively reduces piece, but also big astigmatism areas has elapsed 6mm to eyeglass two sides, further reduces big astigmatism pair
The influence in optic centre region improves the wear comfort of focus eye lens user.
Embodiment 2
The eyeglass of initial designs is identical with the initial designs eyeglass in embodiment 1 in the present embodiment.By u (x, y) generation
Enter formula (1) and formula (4) obtains ζ, R, ξ, η, wherein η=0, ζ, R, ξ, η are substituted into formula (3), and to obtain progressive additional ophthalmically acceptable
The initial rise z of eyeglass.
It is optimized using majorized function (2).
Single order and second-order partial differential coefficient and three rank partial derivatives is asked to obtain R, ζ and ξ of initial designs respectively using central difference method
Above-mentioned amount substitution formula (16) is obtained into the expression formula F of principal curvatures difference square(2), by F(2)It substitutes into formula (28) and obtains
To about c1、c2Binary nonlinear equation group.C is set1、c2It is initially zero, with Levenberg-Marquardt algorithm solution
The root for obtaining Nonlinear System of Equations formula (28) is c10=0.0813 and c20=-0.0007, through trial, take Dynamic gene α=
0.4 substitutes into (29) up to c1=0.03252 and c2=-0.00028.
By c1And c2Value substitute into formula (19) obtain majorized function η (x, y).The distribution of majorized function η (x, y) such as attached drawing 5
Shown, as can be seen from the figure: majorized function η (x, y) has an impact on almost entire eyeglass, but in gradual change passage proximate
The absolute value of majorized function is smaller, i.e., influences on the astigmatism in gradual change channel smaller.
The surface rise of ophthalmic progressive additional lens after η (x, y) substitution formula (3) is optimized.After optimization gradually
It is as shown in Fig. 6 into multifocal ophthalmic lens focal power and astigmatism distribution.
The present embodiment optimization front and back ophthalmic progressive additional lens optical performance parameter is as shown in table 1.Optimize the area Hou Yuanyong
Focal power is -3.90 diopters, and the area Jin Yong focal power is -1.94, and additional optical focal power is 1.96 diopters.Progressive multi-focal after optimization
Point eye lens additional optical focal power has changed 0.04 diopter, in the position of x=-10mm, width of the astigmatism less than 0.25 diopter
Degree reaches 56mm, increases 2mm than initial designs width, and maximum astigmatism reduces 0.26 diopter, about reduces 10.9%, and
The area of big spread area (region that astigmatism is more than or equal to 2 diopters) is by original 66mm2It is reduced to 38mm2, reduce 14mm2,
About reduce 42%.Compared with initial designs, the eyeglass after optimization effectively reduces eyeglass maximum astigmatism, reduces big spread area
Area, and the optical property in regions other on eyeglass is had little effect.
Ophthalmic progressive additional lens optical performance parameter in 1 Examples 1 and 2 of table
The embodiment of the present invention 1 and 2 the results show that majorized function (1) and majorized function (2) can reduce improve it is progressive
The maximum astigmatism of multifocal ophthalmic lens, majorized function (1) can significantly elapse big spread area to lens edge, majorized function
(2) area of big spread area can be substantially reduced.
Claims (4)
1. a kind of preparation method of the ophthalmic progressive additional lens of center of curvature optimization, is first calculated the surface of initial lens
Rise, the center of curvature coordinate of initial lens are (ξ, η, ζ), and the radius of curvature of lens surface is R=R (x, y), the center of curvature
X coordinate be ξ=ξ (x, y), y-coordinate is η=0, and z coordinate is ζ=ζ (x, y), it is characterised in that carry out again following steps plus
Work:
(1) to the majorized function expression formula of the y-coordinate η in the center of curvature coordinate (ξ, η, ζ) of initial lens (1) as follows
It optimizes:
Wherein, sgn (y) is sign function；B is location parameter, and the value range of b is 0.4~1.2；κ is width parameter, and κ's takes
Being worth range is 0.6~1.2；For the bore of eyeglass；Optimized coefficients a1And a2(2) Nonlinear System of Equations calculates as follows
It arrives:
Wherein, J1(a1,a2)=∫ ∫ F(1)Dxdy, F(1)For square of initial lens surface principal curvatures difference, F(1)=(k1-k2)2, and
(k1-k2)2=g-6[r(1+q2)-2pqs+t(1+q2)]2-4g-4(rt-s2),
Wherein,
(2) as follows (3) calculate eyeglass surface rise:
(3) the surface rise machining lens obtained with step (2) obtain a kind of ophthalmically acceptable mirror of progressive additional of center of curvature optimization
Piece.
2. by a kind of ophthalmic progressive additional lens for center of curvature optimization that claim 1 preparation method obtains.
3. a kind of preparation method of the ophthalmic progressive additional lens of center of curvature optimization, first obtains the surface arrow of initial lens
Height, the center of curvature coordinate of initial lens are (ξ, η, ζ), and the radius of curvature of lens surface is R=R (x, y), the center of curvature
X coordinate is ξ=ξ (x, y), and y-coordinate is η=0, and z coordinate is ζ=ζ (x, y), it is characterised in that carries out the processing of following steps again:
(1) to the majorized function expression formula of the y-coordinate η in the center of curvature coordinate (ξ, η, ζ) of initial lens (4) as follows
It optimizes:
In formula, R=R (x, y) is the surface curvature radius of initial lens；Optimized coefficients c1And c2(5) calculate as follows
It arrives:
In formula, α is Dynamic gene, and value range is 0.2~0.8；c10And c20Respectively following formula (6) Nonlinear System of Equations
Root:
In formula, J2(c1,c2)=∫ ∫ F(2)Dxdy, F(2)For square of initial lens surface principal curvatures difference, F(2)=(k1-k2)2, and
(k1-k2)2=g-6[r(1+q2)-2pqs+t(1+q2)]2-4g-4(rt-s2),
Wherein,
(2) as follows (7) calculate eyeglass surface rise:
(3) the surface rise machining lens obtained with step (2) obtain a kind of ophthalmically acceptable mirror of progressive additional of center of curvature optimization
Piece.
4. by a kind of ophthalmic progressive additional lens for center of curvature optimization that claim 3 preparation method obtains.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201710829559.9A CN107632412B (en) | 2017-09-14 | 2017-09-14 | A kind of ophthalmic progressive additional lens and preparation method thereof of center of curvature optimization |
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