CN1779505A - Farsighted lens designing method - Google Patents

Abstract

A method for designing long sight glasses lens includes making the second surface to be scrobicula surface and confirming the first surface according to degree formula of long sight glasses lens, utilizing nonspherical optimizing method to calibrate image difference and naming said method as achievement function including control items and least square method, adjusting central thickness value after each optimizing to decrease increment of edge thickness and using it as initial value of next optimizing, repeating optimization till desired result is achieved.

Description

The spectacles for long sight design method

[technical field]

The invention relates to a kind of spectacles for long sight design method, especially about a kind of spectacles for long sight design method that adopts the aspheric surface design.

[background technology]

Be myopia correction and long sight, lens can be divided into two kinds, and a kind of is the myopia eyeglass, and a kind of is the farsightedness eyeglass.The myopia eyeglass is proofreaied and correct with concavees lens usually, and the farsightedness eyeglass is proofreaied and correct by convex lens usually.

No matter be farsightedness eyeglass or myopia eyeglass, wish that generally lens has the flat performance of light weight, thin thickness and minute surface, and have less aberration, and the preferable lens of performance depend on method for designing spectacle lenses to a great extent.

Adopt the sphere design in the conventional method for designing spectacle lenses, because in the sphere design, can only come aberration correction by adjusting two surface curvature radiuses, will make the lens center thickness thicker thus, outward appearance is very heavy.

The applicant is in No. 93120050 patent of TaiWan, China of application on July 2nd, 2004, disclosed a kind of method for designing of aspheric surface concavees lens, the method for designing of these aspheric surface concavees lens, at first defining lens, not to be close to the one side of eyes be the eyeglass first surface, the one side of being close to eyes is the eyeglass second surface, for making thinner thickness, get first and be the plane, second is adopted the sphere method for designing, adopt the aspheric surface method for designing again, not only can make the effective attenuate of thickness of eyeglass, and make the aberration of eyeglass also obtain good calibration; Only, this aspheric surface negative lens method for designing also not exclusively is applicable to the design of farsightedness eyeglass, if make the aspheric surface convex lens thin thickness of designing, needing first is convex surface, second is the plane, still is close to eyes because of second face, when wearing, eyes more protruding people can touch on the eyeglass, so can not satisfy consumer's requirement.

In view of above shortcoming, be necessary to provide a kind of spectacles for long sight design method of designing better performance.

[summary of the invention]

Order of the present invention is to provide a kind of spectacles for long sight design method of designing better performance.

Spectacles for long sight design method of the present invention, the step of this design farsightedness eyeglass method is as follows: getting second surface earlier is the scrobicula face, first surface is determined according to farsightedness eyeglass number of degrees formula; Then first surface is come aberration correction with the aspheric surface optimization method, described optimization method defines a performance function, this performance function comprises the control item that designing institute is considered, performance function is illustrated as having the function of asphericity coefficient and quadric surface coefficient parameter: this performance function is by damped least square method result of calculation; Behind each the optimization, adjust the center thickness value, make its increment that reduces edge thickness as the initial value of optimizing, loop optimization next time.

Compared with prior art, spectacles for long sight design method of the present invention, second surface adopts the scrobicula face, can avoid eyes to contact with eyeglass; Adopt aspheric surface method for designing first surface, not only can make the effective attenuate of thickness of eyeglass, and make the aberration of eyeglass also obtain good correction; Introduce conic constant in the design, come together to adjust lens performance, the farsightedness eyeglass of design is compared with the sphere farsightedness eyeglass of same specification, preferable performance is arranged by this conic constant and asphericity coefficient; In the optimizing process, considered the influence of the point of inflexion, made the farsightedness eyeglass handling ease after the design.In design, the influence of CONSIDERING EDGE thickness makes the farsightedness eyeglass of designing have suitable edge thickness.

[description of drawings]

Fig. 1 is existing spheric glass synoptic diagram;

Fig. 2 is the aspherical lens synoptic diagram of method for designing spectacle lenses design of the present invention;

Fig. 3 is the aberration diagram after method for designing spectacle lenses design of the present invention is finished;

Fig. 4 is the distortion figure after method for designing spectacle lenses design of the present invention is finished.

[embodiment]

Now in conjunction with specific embodiments spectacles for long sight design method of the present invention is further described:

Spectacles for long sight design method of the present invention, at first defining the one side of not being close to eyes is the eyeglass first surface, the one side of being close to eyes is the eyeglass second surface.Getting first curvature of face radius is R ₁, second curvature of face radius is R ₂, n is an eyeglass material refractive index, t is a center of lens thickness, the index of refraction F of first surface ₁=(n-1)/R ₁, the index of refraction F of second surface ₂=(1-n)/R ₂, the number of degrees of farsightedness eyeglass (diopter) are the back focal length of farsightedness eyeglass gained reciprocal, its formula promptly:

$F_v=\frac{F_1+F_2-\frac{t}{n}{F}_1{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20041005250700102.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{1-\frac{t}{n}{F}_1}$

F _VUnit is 1/ meter, represents with D usually, general 1D=100 degree, and our usual said lens number of degrees are exactly F _VOn duty with 100 value.This lens number of degrees computing formula both had been applicable to that convex lens also were suitable for negative lens.From formula, spectacles for long sight sheet material is certain, and the farsightedness eyeglass number of degrees are by R so ₁, R ₂And the t value decides.

During design, have thin thickness, it need be designed to suitable edge thickness e for making these convex lens.Edge thickness e can not be too little, if too small, cracked easily, if too big, causes the waste of material, gains in weight.Edge thickness e while and center thickness t, first curvature of face radius R ₁, second curvature of face radius R ₂Relevant.During design, calculate the t value, after the t value is determined, by adjusting R by the edge thickness desired value ₁And R ₂Value guarantees that the farsightedness eyeglass number of degrees are constant.R ₁And R ₂Change further have influence on the change of e, for keeping e constant, adjust center thickness t again, after the adjustment, be optimized again, circulation successively is to calculate satisfied asphericity coefficient optimal value.

Designed farsightedness eyeglass wherein at least one surface is an aspheric surface, and wherein the aspheric surface computing formula of aspheric surface employing is

$Z=\frac{C_v{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20041005250700102.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{1+\sqrt{1-{\mathrm{Pc}}_v^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20041005250700102.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+{\mathrm{<figure-callout\; id="4"\; label="Br"\; filenames="A20041005250700102.png"\; state="\{\{state\}\}">Br</figure-callout>}}^4+{\mathrm{<figure-callout\; id="6"\; label="Cr"\; filenames="A20041005250700102.png"\; state="\{\{state\}\}">Cr</figure-callout>}}^6+{\mathrm{Dr}}^8+{\mathrm{Er}}^{10}$

Wherein, Z is the minute surface degree of depth in the formula, C _vExpression aspheric surface curvature of centre, r represents that any point is to the vertical height at minute surface center on the minute surface, and P is the conic constant value, and B, C, D, E represent aspheric surface high-order term coefficient.

Spectacles for long sight design method of the present invention is that the convex lens design process of 4D is an example with the farsightedness eyeglass number of degrees, and its process is as follows:

Existing 4D sphere farsightedness eyeglass synoptic diagram sees also Fig. 1, and wherein this sphere farsightedness eyeglass first curvature of face radius is R ₁=55.08512mm, second curvature of face radius is R ₂=82.59859mm, minute surface center thickness t=6.134mm, minute surface edge thickness e=1.000626, minute surface axial height ah=14.39197, optic diameter D _A=72mm.

We adopt the aspheric surface method for designing to proofread and correct above conventional design, and at first by the method design of sphere design, do not consider the correction of aberration this moment when designing, and getting spectacles for long sight sheet material is plastic cement, gets PC (polycarbonate) herein, its density p=1.25g/mm ³, refractive index n _d=1.586, chromatic dispersion V _d=58.6, optic diameter D _A=72mm.

The design of aspheric surface convex lens, thin and flat for making the eyeglass of designing, needing first of definition is aspheric surface, second is the plane, but in order to protect eyes, second face is taken as the scrobicula face.For making concave surface less, get the number of degrees and be negative 50 degree, i.e. F ₂We are taken as-0.5D, and this moment, second curvature of face radius was with formula F ₂=(1-n)/R ₂, calculate R ₂Be 1172mm, thinner for making eyeglass, definition e=1mm, first curvature of face radius calculates according to number of degrees formula, gets R ₁=132.5mm, t=5.44mm, at this moment, the farsightedness eyeglass is flat and thin, but aberration is bigger.

Then, on the basis of initial designs, optimize first surface, so that proofread and correct the aberration of farsightedness eyeglass with the aspheric surface optimal design.

We are optimized with least square method, earlier definition one performance function

$\mathrm{\&Phi;}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left[\mathrm{Wi}(\mathrm{ei}-\mathrm{ti})\right]}^2=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_i^2$

W wherein _iBe weight factor, its value is taken as W _i＞0, usually to follow the example of be that importance according to the place item decides to weight factor, if the place item is required very strict, then that weight factor can be obtained bigger.M is the integer more than or equal to 1, e _iBe the correction term of being considered, the e that is considered _iItem number, be the numerical value of m.t _iBe desired value, desired value t _iValue, according to e _iSituation and deciding, t usually _iValue be e _iExpectation value, and each available f _i=W _i(e _i-t _i) represent.

In the design of farsightedness eyeglass, the correction term that we are concerned about at first most is aberration e _i, comparatively mild for aberration is controlled on second minute surface, we get the aberration correction of three positions, comprise the oblique fire astigmatism of 0.5 field angle, the oblique fire astigmatism of 0.7 field angle and the oblique fire astigmatism of 1.0 field angle respectively, use e respectively ₁, e ₂, e ₃Represent.The correction factor of another consideration is the distortion of 1.0 field angle, uses e ₄Expression.In addition, also to consider second point of inflexion influence, use e ₅Represent that the judgement of the point of inflexion can be made the second differential value to minute surface height r by minute surface degree of depth s and judges, promptly in the aspheric surface formula r is got second derivative.If there is the point of inflexion curved surface d to occur ²S/dr ²Value the change of sign is arranged, can judge.Last Φ value can be expressed as function (1):

Φ＝W ₁ ²(e ₁-t ₁) ²+W ₂ ²(e ₂-t ₂) ²+W ₃ ²(e ₃-t ₃) ²+W ₄ ²(e ₄-t ₄) ²+W ₅ ²(e ₅-t ₅) ²

(1)

These five square factors all with asphericity coefficient B, C, D, E is relevant with the quadric surface FACTOR P, can be expressed as (P, B, C, D, E) function of five variable elements.In the aspheric surface formula, we get five Variable Designing Of parameters (P, B, C, D, E), this Φ value representation becomes to contain (P, B, C, D, E) function of five variable elements at last.

We are optimized above-mentioned (1) formula, desirable each weight factor W ₁=W ₂=W ₃=W ₄=W ₅=1, desired value t ₁=t ₂=t ₃=t ₄=t ₅=0, Φ value optimum value is controlled at 0 and is optimum range, but generally is difficult to reach, and we can be decided to be the Φ value according to experience is certain limit, and in optimizing process, the Φ value can be more and more littler.

For calculate (P, B, C, D, value E), we adopt damped least square method.Because of designing when initial, each (P, B, C, D E) all has an initial value, and we represent with vector, establish (P, B, C, D, initial value E) they are x ₀=(x ₁₀, x ₂₀, x ₃₀, x ₄₀, x ₅₀), each e ₁, e ₂, e ₃, e ₄, e ₅One initial value is all arranged, and we establish and use f ₀=(f ₁₀, f ₂₀, f ₃₀, f ₄₀, f ₅₀) represent.Value after the optimization is with x=(x ₁, x ₂, x ₃, x ₄, x ₅) expression, aberration f=(f ₁, f ₂, f ₃, f ₄, f ₅) expression.X represents x-x ₀Value, damped least square method separate the value that can solve variable quantity, the concrete formula that damped least square method is separated, promptly

X＝(A ^TA+PI) ^-1A ^Tf ₀

The A five-element five column matrix in the formula, $A_{\mathrm{ij}}=\frac{{\&PartialD;f}_i}{\&PartialD;x_j},$

I, the value of j is from 1 to 5, is f ₁, f ₂, f ₃, f ₄, f ₅Respectively to x ₁, x ₂, x ₃, x ₄, x ₅Ask the partial derivative gained five-element five column matrix, wherein A ^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 above multiplication of matrices computing, can get the operation values of X, passes through x=x ₀+ X can determine the value of x, and then can draw (P, B, C, D, value E) after the correction.

After finishing the optimizing process first time, calculate t=5.441mm, the further e=1.858mm that gets, for making the thick 1mm of being approximately in limit, center thickness t need be deducted the edge thickness increment, promptly reduce 5.441-0.858mm=4.583mm, constant for guaranteeing the farsightedness eyeglass number of degrees, further adjust second index of refraction, for the second time optimizing initial value is t=4.583, and e=0.988mm is optimized again, result after optimizing for the second time is t=4.583, e=1.016.And the like, repeatedly after the loop optimization, can get the edge thickness into 1mm that becomes.

Fig. 2 is the aspheric surface farsightedness eyeglass synoptic diagram after optimizing, and Fig. 3 and Fig. 4 are for optimizing back figure as a result, and oblique fire this moment astigmatism is 0, and the index of refraction error is-0.237D that distortion is 4.371%.At last, determine R according to the number of degrees ₁Value.Result after the farsightedness eyeglass aspheric surface optimal design of its 4D asks for an interview table 1.

Table 1

Specification	The aspheric surface farsightedness eyeglass of design	The sphere farsightedness eyeglass of same specification
			Diopter:	4D
Optic diameter:	72mm

First curvature of face radius:	132.2325mm	55.08512mm
			Second curvature of face radius:	1198.686mm	82.59859mm
The quadric surface constant P:	-5.5079	Do not have
			Asphericity coefficient:	B：-3.1912×10 -7 C：1.2857×10 -10 D：-3.0321×10 -14 E：-9.2340×10 -18	Do not have
Center thickness:	4.567mm	6.134mm
			Edge thickness:	1.001mm	1.000626mm
Axial height:	5.107mm	14.39197mm
			The oblique fire astigmatism:	0	0
The index of refraction error:	-0.237D	-0.236D
			Distortion:	4.371％	3.955％
Quality:	13.558g	19.359g

Compare with the sphere farsightedness eyeglass of same specification, its edge thickness reduces 26%, and axial height reduces 65%, quality alleviates 30%, compares with sphere farsightedness eyeglass, has obviously reduced the thickness and the quality of farsightedness eyeglass, the farsightedness eyeglass is compared with sphere farsightedness eyeglass simultaneously, and is more smooth.

Designed its oblique fire astigmatism of aspheric surface farsightedness eyeglass is 0, and the curvature of field is average index of refraction error, and all in less than 0.25 scope, distortion is less than in 4.4% scope, so this spectacles for long sight design method all can meet the demands.

Claims (5)

1. spectacles for long sight design method, described farsightedness eyeglass tool first surface and second surface, the step that designs this farsightedness eyeglass is as follows:

Getting second surface is the scrobicula face, and first surface is determined according to farsightedness eyeglass number of degrees formula;

First surface is come aberration correction with the aspheric surface optimization method, and described optimization method defines a performance function, and this performance function comprises the control item that designing institute is considered, performance function is illustrated as having the function of asphericity coefficient and quadric surface coefficient parameter;

This performance function is by damped least square method result of calculation;

After the optimization, adjust the center thickness value, make its increment that reduces edge thickness as the initial value of optimizing, loop optimization next time.

2. spectacles for long sight design method according to claim 1, it is characterized in that: use the aspheric surface formula in the aspheric surface optimization method process that is adopted and calculate, this aspheric surface formula is $z=\frac{c_v{r}^2}{1+\sqrt{1-P{c}_v^2{r}^2}}+{\mathrm{Br}}^4+{\mathrm{Cr}}^6+{\mathrm{Dr}}^8+{\mathrm{Er}}^{10}$

Wherein, z is the minute surface degree of depth, C _vExpression aspheric surface curvature of centre, r represents that any point is to the vertical height at minute surface center on the minute surface, and P is the conic constant value, and B, C, D, E represent aspheric surface high-order term coefficient.

3. spectacles for long sight design method as claimed in claim 2 is characterized in that: this performance function is

$\mathrm{\&Phi;}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left[\mathrm{Wi}(\mathrm{ei}-\mathrm{ti})\right]}^2$

Wherein Φ represents performance function value, W _iBe weight factor, m is the integer more than or equal to 1, e _iBe the correction term of being considered, t _iBe desired value.

4. spectacles for long sight design method as claimed in claim 3 is characterized in that: e in this performance function _iGet five, be respectively 0.5 field angle oblique fire astigmatism e ₁, 0.7 field angle oblique fire astigmatism e ₂, 1.0 field angle oblique fire astigmatism e ₃, the distortion e ₄, point of inflexion e ₅, its formula is

Φ＝W ₁ ²(e ₁-t ₁) ²+W ₂ ²(e ₂-t ₂) ²+W ₃ ²(e ₃-t ₃) ²+W ₄ ²(e ₄-t ₄) ²+W ₅ ²(e ₅-t ₅) ²。

5. spectacles for long sight design method as claimed in claim 4 is characterized in that: the point of inflexion of described non-spherical surface is for to ask the second derivative gained to the aspheric surface computing formula.

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