CN114994947A - Surface shape design method of progressive power lens and progressive power lens - Google Patents
Surface shape design method of progressive power lens and progressive power lens Download PDFInfo
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Abstract
The invention discloses a surface shape design method of a progressive focal power lens and the progressive focal power lens, wherein the design method comprises the following steps: s1, designing a Zernike polynomial as a surface shape description equation of the progressive power lens, and setting a to-be-determined progressive surface coefficient in the equation; obtaining an average curvature formula H of the investigation point according to a free-form surface equation; and setting the mean curvature distribution P for discrete sample points on the progressive power lens 0 And a weighting factor α for the power accuracy; s2, establishing an evaluation function: j (u) ═ jk ═ α (x, y) (H-P) 0 (x,y)) 2 ]dA; and S3, obtaining the optimized progressive surface coefficient by solving the minimum value of the evaluation function. According to the method, an optimal coefficient solution is found by adjusting the weight coefficient alpha of focal power accuracy and utilizing a least square method; in zernikeThe polynomial is used as a surface shape description equation of the progressive power lens, the algorithm is reliable, and the effect of designing the progressive power lens is ideal.
Description
Technical Field
The invention relates to the field of lens design, in particular to a surface shape design method of a progressive power lens and the progressive power lens.
Background
The power of the progressive lens is gradually and smoothly changed, so that the clear vision of the upper and lower areas of the lens can be provided simultaneously, and the progressive lens has the advantage of being clear continuously from a long distance to a short distance.
For example, chinese patent application publication No. CN 105445956a discloses a method for designing a free-form progressive lens with corrected astigmatism, and a lens, and proposes a method for describing a progressive lens surface shape by using an extended quadric formula, and sets an evaluation function in commercial optical design software Zemax to optimize astigmatism distribution of the lens. Although the proposal solves the problem of surface distribution smoothness and realizes global optimization, the surface shape description equation is relatively complex, and the lens progressive surface is easy to generate local abrupt change. Meanwhile, commercial design software is adopted, and the user without copyright can not directly use the design software.
The above background disclosure is only for the purpose of assisting understanding of the inventive concept and technical solutions of the present invention, and does not necessarily belong to the prior art of the present patent application nor give technical teaching; the above background should not be used to assess the novelty and inventive aspects of the present application in the absence of express evidence that the above disclosure is published prior to the filing date of the present patent application.
Disclosure of Invention
It is an object of the present invention to provide a surface design method for a progressive power lens that is effective without the use of algorithms of commercially available design software.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method of designing a progressive power lens profile, comprising the steps of:
s1, determining the surface shape description formula of the progressive power lens as follows:
Z＝f(x,y)＝∑z i ·w i ，
wherein x and y are coordinates of the investigation point, Z is surface shape description quantity of the investigation point on the progressive power lens, and Z i Is the expression of the ith term in a Zernike polynomial in a Cartesian coordinate system, w i Is corresponding to z i Wherein i has a plurality of preset integer values;
and obtaining an average curvature formula of the investigation point according to a free-form surface equation:
where H is the average curvature of the point of interest,
Z x is the first order partial derivative of Z in the x-axis direction, Z y Is a first order partial derivative of Z in the y-axis direction, Z xy Is the second-order partial derivative of Z in the directions of x and y axes, Z xx Is the second-order partial derivative of Z in the x-axis direction, Z yy Is the second order partial derivative of Z in the direction of the y axis;
setting a coefficient matrix aiming at discrete sample points on the gradual change power lens, wherein the coefficient matrix comprises an average curvature distribution P0 and a weight coefficient alpha of power accuracy;
s2, establishing an evaluation function:
J(u)＝∫[α(x，y)(|H-P 0 (x，y)|) γ ]dA，
where α (x, y) is a weighting factor for the power accuracy at the point of interest (x, y), P 0 (x, y) is the average curvature target at the point of investigation (x, y), dA denotes integrating the region a, γ is a fraction or integer;
s3, obtaining an optimized progressive surface coefficient data set W ═ W by solving the minimum value of the evaluation function i ]。
Further, the step of optimizing the progressive surface coefficient data set W includes:
according to the evaluation function in step S2, the evaluation function for obtaining discrete sample points is:
where M is the total number of discrete sample points, α m (x, y) is a weighting factor for the power accuracy at the mth discrete sample point, P 0m (x, y) is the average curvature target at the m-th discrete sample point, H m (x, y) is the calculated mean curvature at the mth discrete sample point, γ is a fraction or integer;
and obtaining an optimized progressive surface coefficient data set W by solving the minimum value of the evaluation function of the discrete sample points.
Further, γ takes a value of 2.
Further, according to the evaluation function at the discrete sample point, a matrix a is defined, and the matrix element of the matrix a is a partial derivative formula of the evaluation function at the mth discrete sample point to the nth progressive surface coefficient in the progressive surface coefficient data set W:
according to the matrix form solved by the least square method, the following results are obtained: x ═ A T A) -1 A T f 0 Wherein A is T Is a transposed matrix of the matrix A, [ 2 ]] -1 Representing an inverse matrix, f 0 Represents the initial value before optimization by presetting the initial value W of the progressive surface coefficient data set 0 And then obtaining;
calculating an optimized progressive surface coefficient data set W by the following formula: w ═ W 0 +X。
Further, the data set of i is a continuous integer set or a discrete integer set; or,
the data set of i has more than 5 data or more than 8 data or more than 10 data or more than 12 data.
Further, the average curvature distribution P of the coefficient matrix is set 0 Comprises the following steps:
designing a desired power for each discrete sample point on the progressive power lens;
converting to obtain the expected average curvature of each discrete sample point according to the following formula to obtain the average curvature distribution P 0 ：
The power is (n _ index-1) the mean curvature, where n _ index is the refractive index of the lens material.
Further, after step S3, the method further includes checking the surface shape description formula:
the optimized progressive surface coefficient data set W is [ W ═ W i ]Substituting the formula Z ═ f (x, y) ═ Σ Z into the surface shape description i ·w i Obtaining the average curvature of each investigation point on the progressive focal power lens according to the free-form surface equation;
drawing an average curvature distribution diagram of the gradually-changed focal power lens;
and the average curvature distribution P in the set coefficient matrix 0 Comparing the corresponding average curvature distribution maps, and if the similarity reaches a preset threshold value, passing the verification; otherwise, adjusting the weight coefficient alpha of the power accuracy, and re-executing the steps S2-S3 to obtain a new optimized progressive surface coefficient data set W [ W ] W [ [ i ]。
Further, the weighting factor α for adjusting the power accuracy includes:
and determining a distribution area with difference, and increasing the weight coefficient alpha of the power accuracy corresponding to the area.
Further, determining a surface shape describing the progressive power lens in the first 10 terms of a zernike polynomial:
wherein the first 10 terms of the zernike polynomial are: z is a radical of 1 ＝1，z 2 ＝y，z 3 ＝x，z 4 ＝2xy，z 5 ＝2(x 2 +y 2 )-1，z 6 ＝x 2 -y 2 ，z 7 ＝3x 2 y-y 3 ，z 8 ＝3y(x 2 +y 2 )-2y，z 9 ＝3x(x 2 +y 2 )-2x，z 10 ＝x 3 -3xy 2 。
According to another aspect of the present invention, there is provided a progressive power lens designed based on the surface shape design method as described above.
The technical scheme provided by the invention has the following beneficial effects: providing a Zernike polynomial as a description equation of the surface shape of the progressive lens, and describing a power distribution target in a discretization grid mode; at the node position of each discretization grid, an evaluation function meeting the focal power distribution target is provided according to a free-form surface principal curvature calculation formula; by adjusting the weight coefficient of focal power accuracy and utilizing a least square method, an optimal coefficient solution is found, the algorithm is simple and effective, and the fitness with a design target is good.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of a method for designing a progressive power lens profile according to an exemplary embodiment of the present invention;
FIG. 2 is a schematic diagram of a distribution of discrete sample points on a progressive power lens provided by an exemplary embodiment of the present invention;
FIG. 3 is a schematic representation of the mean curvature contour distribution for designing a progressive power lens provided by an exemplary embodiment of the present invention;
FIG. 4 is a schematic diagram of the contour distribution of the mean curvature of the lens according to the embodiment of the surface shape design method of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Moreover, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, apparatus, article, or device that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or device.
In one embodiment of the present invention, a method for designing a progressive power lens profile is provided, as shown in fig. 1, the method comprising the steps of:
s1, determining the surface shape description formula of the progressive power lens as follows:
Z＝f(x，y)＝∑z i ·w i ，
wherein x and y are coordinates of a survey point, Z is a surface shape description quantity of the survey point on the progressive power lens, and Z is i Is the expression of the ith term, w, in a Zernike polynomial in a Cartesian coordinate system i Is corresponding to z i Wherein i has a plurality of preset integer values;
and obtaining an average curvature formula of the investigation point according to a free-form surface equation:
where H is the average curvature of the point of interest,
Z x is the first order partial derivative of Z in the x-axis direction, Z y Is the first order partial derivative of Z in the y-axis direction, Z xy Is the second-order partial derivative of Z in the directions of x and y axes, Z xx Is the second-order partial derivative of Z in the x-axis direction, Z yy Is the second order partial derivative of Z in the direction of the y axis;
the data set of i may be a continuous integer set, such as a surface shape of a point of interest on the progressive power lens described by expressions of first to tenth terms (also from third to eleventh terms) in a zernike polynomial in a cartesian coordinate system;
the data set of i may also be a discrete integer set, such as a second, fifth, sixth, eighth, and twelfth expression in a zernike polynomial in a cartesian coordinate system to describe the profile of a point of interest on the progressive power lens;
the invention is not limited to the number of data sets that the data set of i has, and the first 10 terms of the zernike polynomial are used as an example to describe the profile of the progressive power lens:
wherein the first 10 terms of the zernike polynomial are: z is a radical of formula 1 ＝1，z 2 ＝y，z 3 ＝x，z 4 ＝2xy，z 5 ＝2(x 2 +y 2 )-1，z 6 ＝x 2 -y 2 ，z 7 ＝3x 2 y-y 3 ，z 8 ＝3y(x 2 +y 2 )-2y，z 9 ＝3x(x 2 +y 2 )-2x，z 10 ＝x 3 -3xy 2 。
Z x The first-order partial derivative of Z in the direction of the x axis corresponds to 10-term expression of Z x1 ＝0，z x2 ＝0，z x3 ＝1，z x4 ＝2y，z x5 ＝4x，z x6 ＝2x，z x7 ＝6xy，z x8 ＝6xy，z x9 ＝9x 2 +3y 2 -2，z x10 ＝3x 2 -3y 2 。
Z y Is the first-order partial derivative of Z in the y-axis direction, and the corresponding 10-term expression is Z y1 ＝0，z y2 ＝1，z y3 ＝0，z y4 ＝2x，z y5 ＝4y，z y6 ＝-2y，z y7 ＝3x 2 -3y 2 ，z y8 ＝3x 2 +9y 1 -2，z y9 ＝6xy，z y10 ＝-6xy。
Z xy Is the second-order partial derivative of Z in the directions of the x axis and the y axis, and the corresponding 10-term expression is Z xy1 ＝0，z xy2 ＝0，z xy3 ＝0，z xy4 ＝2，z xy5 ＝0，z xy6 ＝0，z xy7 ＝6x，z xy8 ＝6x，z xy9 ＝6y，z xy10 ＝-6y。
Z xx The second-order partial derivative of Z in the direction of the x axis corresponds to 10-term expression of Z xx1 ＝0，z xx2 ＝0，z xx3 ＝0，z xx4 ＝0，z xx5 ＝4，z xx6 ＝2，z xx7 ＝6y，z xx8 ＝6y，z xx9 ＝18x，z xx10 ＝6x。
Z yy The second-order partial derivative of Z in the y-axis direction corresponds to a 10-term expression of Z yy1 ＝0，z yy2 ＝0，z yy3 ＝0，z yy4 ＝0，z yy5 ＝4，z yy6 ＝-2，z yy7 ＝-6y，z yy8 ＝18y，z yy9 ＝6x，z yy10 ＝-6x。
The above expressions are compiled into the following table:
| number of items | Expression of z | z x | z y | z xy | z xx | z yy | |
| Item 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| Item 2 | |
0 | 1 | 0 | 0 | 0 | |
| Item 3 | x | 1 | 0 | 0 | 0 | 0 | |
| Item 4 | 2xy | 2y | 2x | 2 | 0 | 0 | |
| Item 5 | 2(x 2 +y 2 )-1 | | 4y | 0 | 4 | 4 | |
| Item 6 | x 2 -y 2 | 2x | - |
0 | 2 | -2 | |
| Item 7 | 3x 2 y-y 3 | 6xy | 3x 2 -3y 2 | 6x | 6y | -6y | |
| Item 8 | 3y(x 2 +y 2 )-2y | 6xy | 3x 2 +9y 2 -2 | 6x | 6y | 18y | |
| Item 9 | 3x(x 2 +y 2 )-2x | 9x 2 +3y 2 -2 | 6xy | 6y | 18x | 6x | |
| Item 10 | x 3 -3xy 2 | 3x 2 -3y 2 | -6xy | -6y | 6x | -6x |
In the above-mentioned formula of the mean curvature of the investigation point,
setting a coefficient matrix aiming at discrete sample points on the gradual change power lens, wherein the coefficient matrix comprises an average curvature distribution P0 and a weight coefficient alpha of power accuracy; specific mean curvature distribution P 0 The setting step comprises:
designing the expected focal power of each discrete sample point on the progressive power lens, as shown in fig. 2, determining the discrete points uniformly distributed on the lens, wherein the denser the discrete points are, the larger the calculation task amount is, the higher the design precision is, otherwise, the smaller the calculation task amount is, the lower the design precision is, and designing the expected focal power at each discrete point, which is a design target and is called a focal power target;
the desired mean curvature for each discrete sample point is transformed, referred to as a mean curvature target, to obtain a mean curvature distribution P0, according to the following equation:
the power is (n _ index-1) the mean curvature, where n _ index is the refractive index of the lens material.
It is an object of embodiments of the invention to determine the progressive surface coefficient w 1 ，w 2 ，w 3 ，w 4 ，w 5 ，w 6 ，w 7 ，w 8 ，w 9 ，w 10 I.e. determining the surface shape description Z at any point on the progressive power lens, is equivalent to determining the average curvature/power at any point on the progressive power lens.
S2, establishing an evaluation function:
J(u)＝∫[α(x，y)(|H-P 0 (x，y)|) γ ]dA，
where α (x, y) is a weighting factor for the power accuracy at the point of interest (x, y), P 0 (x, y) is an average curvature target at the investigation point (x, y), dA represents the integration of the region a, γ is a fraction or an integer, γ is 2 in this embodiment, and γ is an odd number in other embodiments, H-P needs to be performed 0 (x, y) the absolute value is found.
S3, obtaining an optimized progressive surface coefficient data set W ═ W by solving the minimum value of the evaluation function i ]And i is 1 to 10.
The step of optimizing the progressive surface coefficient data set W specifically includes:
according to the evaluation function in step S2, the evaluation function of obtaining discrete sample points is:
where M is the total number of discrete sample points, α m (x, y) is a weighting factor for the power accuracy at the mth discrete sample point, P 0m (x, y) isMean curvature target at the mth discrete sample point, H m (x, y) is the calculated mean curvature at the mth discrete sample point;
and obtaining an optimized progressive surface coefficient data set W by solving the minimum value of the evaluation function at each discrete sample point. The method comprises the following specific steps:
solving the minimum value problem of the evaluation function can be converted into a problem of how to adjust the progressive surface coefficient W to be determined in the zernike polynomial so that the sum of the evaluation values of all the sample points is minimum, which is a typical least square solution problem.
Defining a matrix A according to the evaluation function at the discrete sample point, wherein the matrix elements of the matrix A are the partial derivative formula of the evaluation function at the mth discrete sample point to the nth progressive surface coefficient in the progressive surface coefficient data set W:
obtaining the following matrix form according to the least square method: x ═ A T A) -1 A T f 0 Wherein X is the optimized increment of the progressive surface coefficient, A T Is a transposed matrix of the matrix A] -1 Representing an inverse matrix;
f 0 represents the initial value before optimization by presetting the initial value W of the progressive surface coefficient data set 0 And then obtaining; assume any given initial Zernike polynomial coefficient (i.e., progressive surface coefficient w) 1 ，w 2 ，w 3 ，w 4 ，w 5 ，w 6 ，w 7 ，w 8 ，w 9 ，w 10 ) Respectively as follows: w 0 ＝[0，0，0，0，-0.01，0，0，0，0，0]Correspondingly obtaining expressions of Z and H, and substituting the coordinates of each discrete sample point into the expression of H to obtain H m The values of (x, y), and the weighting coefficients of the power accuracy and the average curvature target for each discrete sample point are pre-designed known values, so substituting f (W) into the function can find f 0 。
Calculating an optimized progressive surface coefficient data set W by the following formula: w ═ W 0 +X。
The embodiment also provides a verification operation on the surface shape description formula:
determining uniformly distributed discrete points on the lens, and designing a desired optical power (optical power target) at each discrete point;
according to the formula, the power is (n _ index-1) the mean curvature, where n _ index is the refractive index of the lens material, the desired mean curvature (mean curvature target) of each discrete sample point is obtained by conversion to obtain a mean curvature distribution P0, the mean curvature contour is shown in fig. 3, and the data of the specific target mean curvature distribution P0 is shown as follows:
the data for the specific power accuracy weighting factor α is as follows:
assume initial W 0 ＝[0，0，0，0，-0.01，0，0，0，0，0]According to the calculation steps of the embodiment, the progressive surface coefficient data set is obtained by optimization:
W＝[0.00000000e+00，0.00000000e+00，0.00000000e+00，8.65857171e-05，-1.58094726e-03，2.87680903e-04，3.13935801e-06，-3.01516933e-06，1.92940098e-07，-7.91390533e-09]
substituting the optimized progressive surface coefficient data set W into a surface shape description formula Z ═ f (x, y) ═ Σ Z i ·w i Obtaining the average curvature of each investigation point on the progressive power lens according to the free-form surface shape equation;
plotting the mean curvature profile of the progressive power lens, as shown in fig. 4;
comparing it with the average curvature distribution P in the set coefficient matrix 0 Is correspondingly provided withComparing the average curvature distribution maps (as shown in fig. 3), and if the similarity reaches a preset threshold, the verification is passed; otherwise, adjusting the weight coefficient alpha of the power accuracy, and re-executing the steps S2-S3 to obtain a new optimized progressive surface coefficient data set W [ W ] W [ [ i ]。
The idea of specifically adjusting the weight coefficient alpha for adjusting the accuracy of the focal power is as follows: and determining a distribution area with difference, and increasing the weight coefficient alpha of the power accuracy corresponding to the area.
The invention discloses a design method of a progressive power lens, which provides a surface shape description equation adopting a Zernike polynomial as a progressive lens, and comprises a plurality of coefficients to be determined; meanwhile, describing the focal power distribution target in a discretization grid mode; at the node position of each discretization grid, an evaluation function which meets the focal power distribution target is provided according to a free-form surface principal curvature calculation formula, and the evaluation function comprises a plurality of unknown coefficients in a surface shape description equation; then, by continuously adjusting the weight coefficient of the focal power accuracy, an optimal coefficient solution is found by using a least square method, so that the sum of evaluation functions of all the sample points is minimum.
In this embodiment, as can be seen from comparing fig. 4 and fig. 3, the surface shape obtained by optimization is subjected to inverse calculation of the curvature distribution map, and is matched with the target distribution map very well, thereby verifying the reliability of the algorithm.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The foregoing is directed to embodiments of the present application and it is noted that numerous modifications and adaptations may be made by those skilled in the art without departing from the principles of the present application and are intended to be within the scope of the present application.
Claims (10)
1. A method for designing a progressive power lens profile, comprising the steps of:
s1, determining the surface shape description formula of the progressive power lens as follows:
wherein x and y are coordinates of a survey point, Z is a surface shape description quantity of the survey point on the progressive power lens, and Z is i Is the expression of the ith term in a Zernike polynomial in a Cartesian coordinate system, w i Is corresponding to z i Wherein i has a plurality of preset integer values;
and obtaining an average curvature formula of the investigation point according to a free-form surface equation:
where H is the average curvature of the point of interest,
Z x is the first order partial derivative of Z in the x-axis direction, Z y Is a first order partial derivative of Z in the y-axis direction, Z xy Is the second-order partial derivative of Z in the directions of x and y axes, Z xx Is the second order partial derivative of Z in the x-axis direction, Z yy Is the second order partial derivative of Z in the direction of the y axis;
and to progressive power lensesDiscrete sample points, setting a coefficient matrix comprising an average curvature distribution P 0 And a weighting factor α for power accuracy;
s2, establishing an evaluation function:
J(u)＝∫[α(x,y)(|H-P 0 (x,y)|) γ ]dA，
where α (x, y) is a weighting factor for the power accuracy at the point of interest (x, y), P 0 (x, y) is the average curvature target at the point of investigation (x, y), dA denotes the integration of the region A, γ is a fraction or integer;
s3, obtaining an optimized progressive surface coefficient data set W ═ W by solving the minimum value of the evaluation function i ]。
2. The progressive power lens surface shape design method according to claim 1, wherein the step of optimizing the progressive surface coefficient data set W comprises:
according to the evaluation function in step S2, the evaluation function for obtaining discrete sample points is:
where M is the total number of discrete sample points, α m (x, y) is a weighting factor for the power accuracy at the mth discrete sample point, P 0m (x, y) is the average curvature target at the m-th discrete sample point, H m (x, y) is the calculated mean curvature at the mth discrete sample point, γ is a fraction or integer;
and obtaining an optimized progressive surface coefficient data set W by solving the minimum value of the evaluation function of the discrete sample points.
3. The method of designing a progressive power lens profile according to claim 2, wherein γ is 2.
4. The method of designing a progressive power lens profile according to claim 2, wherein a matrix a is defined according to the evaluation function at the discrete sample points, and the matrix elements thereof are a partial derivative formula of the evaluation function at the mth discrete sample point to the nth progressive coefficient in the progressive coefficient data set W:
obtaining the following matrix form according to the least square method: x ═ A T A) -1 A T f 0 Wherein A is T Is a transposed matrix of the matrix A] -1 Representing an inverse matrix, f 0 Represents an initial value before optimization by presetting an initial value W of a progressive surface coefficient data set 0 Thus obtaining the compound;
calculating an optimized progressive surface coefficient data set W by the following formula: w ═ W 0 +X。
5. The method for designing a progressive power lens profile according to claim 1, wherein the data set of i is a continuous integer set or a discrete integer set; or,
the data set of i has more than 5 data or more than 8 data or more than 10 data or more than 12 data.
6. Method for designing the surface shape of a progressive power lens according to claim 1, characterized in that the mean curvature distribution P of the coefficient matrix is set 0 Comprises the following steps:
designing a desired power for each discrete sample point on the progressive power lens;
converting to obtain the expected average curvature of each discrete sample point according to the following formula to obtain the average curvature distribution P 0 ：
The power is (n _ index-1) mean curvature, wherein n _ index is the refractive index of the lens material.
7. The method for designing a progressive power lens profile according to claim 1, further comprising verifying the profile description formula after step S3:
setting the optimized progressive surface coefficient data set W as [ W ═ W i ]Substituting the formula Z ═ f (x, y) ═ Σ Z into the surface shape description i ·w i Obtaining the average curvature of each investigation point on the progressive focal power lens according to the free-form surface equation;
drawing an average curvature distribution diagram of the gradually-changed focal power lens;
and the average curvature distribution P in the set coefficient matrix 0 Comparing the corresponding average curvature distribution maps, and if the similarity reaches a preset threshold value, passing the verification; otherwise, adjusting the weight coefficient alpha of the power accuracy, and re-executing the steps S2-S3 to obtain a new optimized progressive surface coefficient data set W [ W ] W [ [ i ]。
8. The method for designing a progressive power lens profile according to claim 7, wherein the weighting factor α for adjusting the power accuracy comprises:
and determining a distribution area with difference, and increasing the weight coefficient alpha of the power accuracy corresponding to the area.
9. The method of designing a progressive power lens form according to claim 1, wherein the determination of the surface form describing the progressive power lens in the first 10 terms of a zernike polynomial:
wherein the first 10 terms of the zernike polynomial are: z is a radical of 1 ＝1，z 2 ＝y，z 3 ＝x，z 4 ＝2xy，z 5 ＝2(x 2 +y 2 )-1，z 6 ＝x 2 -y 2 ，z 7 ＝3x 2 y-y 3 ，z 8 ＝3y(x 2 +y 2 )-2y，z 9 ＝3x(x 2 +y 2 )-2x，z 10 ＝x 3 -3xy 2 。
10. A progressive power lens designed based on the surface shape design method according to any one of claims 1 to 9.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116679465A (en) * | 2023-08-03 | 2023-09-01 | 苏州派视光学有限公司 | Double-sided progressive addition lens and design method thereof |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050052615A1 (en) * | 2003-09-05 | 2005-03-10 | Regents Of The University Of Minnesota | Multifocal optical device design |
| US20050083482A1 (en) * | 2001-12-05 | 2005-04-21 | Sola International Holdings, Ltd | Balanced progressive lens |
| CN1809779A (en) * | 2003-06-26 | 2006-07-26 | 埃西勒国际通用光学公司 | Method for designing progressive addition lenses |
| CN103080818A (en) * | 2010-07-16 | 2013-05-01 | 卡尔蔡斯光学公司 | Wavefront optimized progressive lens |
| CN106932921A (en) * | 2017-05-05 | 2017-07-07 | 上海理工大学 | Progressive additional free surface lens method of evaluating performance |
| CN109975994A (en) * | 2017-12-27 | 2019-07-05 | 鸿富锦精密工业（深圳）有限公司 | Eye lens design device and eye lens design method |
| CN110705040A (en) * | 2019-09-11 | 2020-01-17 | 中国科学院光电技术研究所 | Method for solving primary and secondary mirror offset error quantity based on Zernike polynomial coefficient and least square method |
| CN112394508A (en) * | 2020-11-30 | 2021-02-23 | 中国科学院光电技术研究所 | Debugging method based on second-order sensitivity matrix method |
-
2022
- 2022-07-12 CN CN202210816994.9A patent/CN114994947A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050083482A1 (en) * | 2001-12-05 | 2005-04-21 | Sola International Holdings, Ltd | Balanced progressive lens |
| CN1809779A (en) * | 2003-06-26 | 2006-07-26 | 埃西勒国际通用光学公司 | Method for designing progressive addition lenses |
| US20050052615A1 (en) * | 2003-09-05 | 2005-03-10 | Regents Of The University Of Minnesota | Multifocal optical device design |
| CN103080818A (en) * | 2010-07-16 | 2013-05-01 | 卡尔蔡斯光学公司 | Wavefront optimized progressive lens |
| CN106932921A (en) * | 2017-05-05 | 2017-07-07 | 上海理工大学 | Progressive additional free surface lens method of evaluating performance |
| CN109975994A (en) * | 2017-12-27 | 2019-07-05 | 鸿富锦精密工业（深圳）有限公司 | Eye lens design device and eye lens design method |
| CN110705040A (en) * | 2019-09-11 | 2020-01-17 | 中国科学院光电技术研究所 | Method for solving primary and secondary mirror offset error quantity based on Zernike polynomial coefficient and least square method |
| CN112394508A (en) * | 2020-11-30 | 2021-02-23 | 中国科学院光电技术研究所 | Debugging method based on second-order sensitivity matrix method |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116679465A (en) * | 2023-08-03 | 2023-09-01 | 苏州派视光学有限公司 | Double-sided progressive addition lens and design method thereof |
| CN116679465B (en) * | 2023-08-03 | 2023-10-13 | 苏州派视光学有限公司 | Double-sided progressive addition lens and design method thereof |
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