CN115202069A - Design method of progressive mirror capable of conveniently adjusting maximum astigmatism distribution area - Google Patents

Design method of progressive mirror capable of conveniently adjusting maximum astigmatism distribution area Download PDF

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CN115202069A
CN115202069A CN202210440279.XA CN202210440279A CN115202069A CN 115202069 A CN115202069 A CN 115202069A CN 202210440279 A CN202210440279 A CN 202210440279A CN 115202069 A CN115202069 A CN 115202069A
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lens
sample point
coefficients
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谢公晚
谢公兴
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Mingyue Lens Co ltd
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Mingyue Lens Co ltd
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    • G—PHYSICS
    • G02—OPTICS
    • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
    • G02C7/00—Optical parts
    • G02C7/02—Lenses; Lens systems ; Methods of designing lenses
    • G02C7/024—Methods of designing ophthalmic lenses
    • G02C7/028—Special mathematical design techniques
    • G—PHYSICS
    • G02—OPTICS
    • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
    • G02C7/00—Optical parts
    • G02C7/02—Lenses; Lens systems ; Methods of designing lenses
    • G02C7/06—Lenses; Lens systems ; Methods of designing lenses bifocal; multifocal ; progressive
    • G02C7/061—Spectacle lenses with progressively varying focal power
    • G02C7/063—Shape of the progressive surface

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Abstract

The invention provides a design method of a progressive mirror for conveniently adjusting a maximum astigmatism distribution area, which comprises the steps of firstly establishing an evaluation function about focal power accuracy and astigmatism minimization; secondly, providing a set of surface shape description equations containing a plurality of unknown coefficients; and finally, uniformly distributed discretization points on the lens are used as sample points, an evaluation function is constructed by combining control coefficients, and the optimal coefficient solution of the surface shape description equation is found by using a least square method for the evaluation function, so that the sum of the evaluation functions of all the sample points is minimum. The method has the advantages that the smoothness of the excessive focal power can be guaranteed; meanwhile, the calculation is simple and the speed is high; furthermore, the maximum astigmatism distribution region can be easily adjusted by adjusting the control coefficient.

Description

Design method of progressive mirror capable of conveniently adjusting maximum astigmatism distribution area
Technical Field
The invention relates to a design method of a progressive lens, in particular to a design method of a progressive lens convenient for adjusting a maximum astigmatism distribution area, and belongs to the technical field of optical lenses.
Background
It is known that the progressive lens can meet the requirements of distance vision and near vision at the same time, and can avoid the defects of fracture and the like when the distance vision and the near vision are converted by a double-lens and the like, so that the progressive lens is increasingly widely applied. Generally, the progressive lens uses a free-form surface to realize continuous variation of the focal power, and a transition zone is continuously and gradually increased by the diopter to realize the natural connection between the surface type and the diopter of a far vision zone and a near vision zone, so that the progressive lens can correct the vision at all visual fields by using only one lens and provide a continuous clear vision from far to near.
The surface of the progressive lens can be generally divided into four parts, namely a far vision zone, a near vision zone, an astigmatism zone and a progressive zone (namely a transition zone), wherein the far vision zone is positioned in a wide area of the upper half part of the progressive lens, and can correct the far vision ability when human eyes are in a relaxed and head-up state, so as to provide a clear and wide visual field; the near vision zone is positioned at the lower half part of the progressive lens and can be used for correcting the vision; the progressive area is positioned between the near vision area and the far vision area and is a transition area with continuously changed refractive power, so that the natural connection between the surface shapes and diopters of the far vision area and the near vision area can be realized, and the visual fields at different distances from far to near can be clearly imaged without fracture; the progressive zone is flanked by astigmatism zones, which cause distortion of the viewing object when the line of sight moves towards the astigmatism zones, the degree of distortion being related to the design and addition of the progressive lens. Thus, anamorphic astigmatism is a key problem that is difficult to overcome in progressive lenses, and although a properly fitted progressive zone can give the wearer clear vision, a certain degree of image distortion will occur on both sides of the progressive zone, the degree and direction of distortion depending on the lens design and the power of the addition, and the distortion of image quality will be more pronounced the farther the eye moves away from the central area of the available progressive zone.
The search finds that Chinese patent with publication number CN102419476B discloses an optimization method for reducing astigmatism of a progressive multifocal lens, the method adopts a global astigmatism optimization method, and adds initial vector height distribution data and vector height distribution data of a new free-form surface to obtain lens surface vector height distribution data after astigmatism optimization. However, in the above technical solution, surface shape optimization is performed for a local area with large astigmatism, and the correlation between points cannot be considered, so that the possibility of realizing global optimization is reduced.
CN107065220B discloses a design method of a personalized free-form surface progressive mirror with a matched and optimized mirror frame, which is based on a variation-difference mathematical method, introduces a contour function of the mirror frame of a glasses, optimizes astigmatism of a lens in a lens optical area limited by the mirror frame, realizes the design of the personalized free-form surface progressive mirror, constructs a personalized optimization evaluation function in the process of solving the free-form surface of the progressive mirror by a variation-difference numerical method according to an optometry prescription of a wearer in combination with the personalized requirements of the contour shape, wearing habits and the like of the mirror frame selected by the wearer during design, simplifies the structures of spherical power and an astigmatism weight function, effectively reduces the astigmatism in the mirror frame area while obtaining the required spherical power design distribution, enables the astigmatism change gradient to be smaller, enables the distribution to be softer, improves the working performance of the effective visual area of the lens, and improves the comfort level of the wearer. The two patents adopt different surface shape description modes and different optimization processes, but the optimization efficiency is low.
Disclosure of Invention
The invention provides a design method of a progressive mirror, which is convenient for adjusting the maximum astigmatism distribution area and overcomes the defects of the prior art.
The invention provides a design method of a progressive mirror convenient for adjusting a maximum astigmatism distribution area, which comprises the following steps:
s1, establishing an evaluation function related to focal power accuracy and astigmatism minimization;
s2, providing a set of surface shape description equations containing a plurality of unknown coefficients;
and S3, uniformly distributed discretization points on the lens are used as sample points, an evaluation function is constructed by combining control coefficients, and the optimal coefficient solution of the surface shape description equation is found by using a least square method for the evaluation function, so that the sum of the evaluation functions of all the sample points is minimum.
The method comprises the steps of establishing a set of evaluation functions comprising unknown coefficients of the surface shape to be solved and control coefficients, and finding the minimum value of the evaluation functions by using a least square method; so that the distribution area of the maximum astigmatism can be conveniently adjusted by adjusting the control coefficient.
The further optimized technical scheme of the invention is as follows:
further, the merit function is as follows:
Figure 45667DEST_PATH_IMAGE002
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE003
are all the control coefficients of the electric motor,
Figure 335834DEST_PATH_IMAGE004
the weight coefficients are controlled for the astigmatism distribution,
Figure DEST_PATH_IMAGE005
is a weighting factor for the power accuracy,
Figure 947557DEST_PATH_IMAGE006
in order to be the power distribution coefficient,His the mean curvature of the sample points and
Figure DEST_PATH_IMAGE007
，Kis a Gaussian curvature of a sample point and
Figure 323174DEST_PATH_IMAGE008
，k 1 、k 2 all are the principal curvatures of the sample points, x, y are the coordinates of the sample points, respectively, a is the minute area, and dA represents the integration for the minute area.
Further, the surface shape description equation is as follows:
Figure 540529DEST_PATH_IMAGE010
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE011
、
Figure 685203DEST_PATH_IMAGE012
、
Figure DEST_PATH_IMAGE013
、
Figure 736335DEST_PATH_IMAGE014
、
Figure DEST_PATH_IMAGE015
、
Figure 333670DEST_PATH_IMAGE016
all are the coefficients to be solved of the surface shape description equation.
In the step S3, the vector height equation of the surface shapezAssume definition
Figure DEST_PATH_IMAGE017
、
Figure 495661DEST_PATH_IMAGE017
、
Figure 229262DEST_PATH_IMAGE018
、
Figure DEST_PATH_IMAGE019
、
Figure 716875DEST_PATH_IMAGE020
The distribution is first and second partial differential in x, y directions, then, from the free-form surface equation, the mean curvature and gaussian curvature of each sample point can be known:
Figure 129402DEST_PATH_IMAGE022
Figure 555136DEST_PATH_IMAGE024
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE025
、
Figure 674402DEST_PATH_IMAGE025
、
Figure 660812DEST_PATH_IMAGE026
、
Figure DEST_PATH_IMAGE027
、
Figure 763897DEST_PATH_IMAGE028
first and second partial differentials in the x and y directions, respectively;
Figure DEST_PATH_IMAGE029
is an intermediate variable, and
Figure 267691DEST_PATH_IMAGE030
。
the above formula for obtaining H and K by the relative differentiation of z is a common surface-shape description formula, and is not described one by one here.
Thus, the minimum value problem of solving the evaluation function is converted into a problem of how to adjust the undetermined coefficient of the surface shape description equation so that the sum of evaluation function evaluation values of all sample points is minimum, which is a typical least square solution problem.
In the step 3, it is assumed that the 6 coefficients to be solved of the aspheric surface are respectively
Figure DEST_PATH_IMAGE031
、
Figure 444726DEST_PATH_IMAGE032
、
Figure DEST_PATH_IMAGE033
、
Figure 274141DEST_PATH_IMAGE034
、
Figure DEST_PATH_IMAGE035
、
Figure 333364DEST_PATH_IMAGE036
At each sample pointThe merit function may be expressed by the following formula:
Figure 234324DEST_PATH_IMAGE038
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE039
the weighting coefficients are controlled for the astigmatism distribution of the ith sample point on the lens,
Figure 531444DEST_PATH_IMAGE040
is the mean curvature of the ith sample point on the lens,
Figure DEST_PATH_IMAGE041
is the gaussian curvature of the ith sample point on the lens,
Figure 263253DEST_PATH_IMAGE042
is a weighting factor for the power accuracy of the ith sample point on the lens,
Figure DEST_PATH_IMAGE043
is the power target value for the ith sample point on the lens,
Figure 75351DEST_PATH_IMAGE044
as a merit function for the ith sample point on the lens,
Figure 100002_DEST_PATH_IMAGE045
namely, it is
Figure 920947DEST_PATH_IMAGE046
，
Figure DEST_PATH_IMAGE047
Namely equivalent to
Figure 197208DEST_PATH_IMAGE041
，
Figure 571688DEST_PATH_IMAGE048
Namely equivalent to
Figure DEST_PATH_IMAGE049
，
Figure 605503DEST_PATH_IMAGE050
Namely equivalent to
Figure 113845DEST_PATH_IMAGE040
，
Figure DEST_PATH_IMAGE051
Namely equivalent to
Figure 916716DEST_PATH_IMAGE043
；
Defining a matrix A, the elements of which are:
Figure DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 258836DEST_PATH_IMAGE054
in order to be a differential sign, the sign of the differential,
Figure DEST_PATH_IMAGE055
in order to evaluate the function of the measurement,
Figure 514368DEST_PATH_IMAGE056
is an independent variable;
then, using the classical least squares formulation, one can obtain:
Figure 173538DEST_PATH_IMAGE058
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE059
is a coefficient matrix from x1 to x6,
Figure 893232DEST_PATH_IMAGE060
represents the transpose of the coefficient matrix a,pwhich is representative of the damping coefficient of the magnetic resonance,Irepresents a matrix of units, and represents a matrix of units,
Figure DEST_PATH_IMAGE061
representing an initial value before optimization;
presetting an initial value of aspheric coefficient as
Figure 140674DEST_PATH_IMAGE062
Obtaining the optimized aspherical surface coefficient by the following formula
Figure DEST_PATH_IMAGE063
，
Figure 883502DEST_PATH_IMAGE064
。
The actual process of step S3 is to obtain an evaluation function from the discretized sample points, and obtain the optimal coefficient of the surface shape proposed in step S2 by using the least square solution of the evaluation function.
In the step 3, an initial value of the aspheric coefficient is preset
Figure 671329DEST_PATH_IMAGE062
Calculating an initial value of the evaluation function by the following formula
Figure 917634DEST_PATH_IMAGE061
，
Figure DEST_PATH_IMAGE065
。
The final optimization of the invention aims to obtain the aspheric coefficient, so that the final surface shape is known. By adjusting the target coefficient
Figure 601556DEST_PATH_IMAGE046
、
Figure 690735DEST_PATH_IMAGE049
And
Figure 688778DEST_PATH_IMAGE043
the distribution area of the maximum astigmatism is adjusted.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects: the invention provides a global optimization algorithm which can ensure the smoothness of excessive focal power; meanwhile, the calculation is simple and the speed is high; also, the maximum astigmatism distribution area can be conveniently adjusted by adjusting the control coefficient.
Drawings
FIG. 1 is a diagram of the distribution of discrete points in the lens of the present invention.
FIG. 2 is a power distribution, astigmatism weight distribution and power weight distribution of the lens of the present invention.
FIG. 3 is a graph of the power distribution of the lens of the present invention.
FIG. 4 is a distribution diagram of astigmatism weights of the lens according to the present invention.
Fig. 5 is a power weight distribution diagram in the present invention.
FIG. 6 is a contour plot of the power of the lens of the present invention.
FIG. 7 is a contour plot of the spherical light of the lens of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection authority of the present invention is not limited to the following embodiments.
The invention relates to a design method of a progressive mirror capable of conveniently adjusting a maximum astigmatism distribution area, which comprises the following steps of:
s1, establishing an evaluation function
For discrete points of uniform distribution of the lens (see fig. 1), three coefficient matrices are set: p0 (power distribution), α (astigmatism distribution control weight coefficient), β (power accuracy weight coefficient).
An ideal progressive mirror can smoothly vary according to the power profile desired by the user with minimal astigmatism, and thus the following merit functions are proposed:
Figure DEST_PATH_IMAGE067
wherein the content of the first and second substances,k 1 、k 2 are the principal curvatures of the sample points. Note book
Figure 914223DEST_PATH_IMAGE068
H is the mean curvature of the sample points;
Figure 972309DEST_PATH_IMAGE008
and K is the gaussian curvature of the sample point.
Then, there are
Figure 548784DEST_PATH_IMAGE002
In the formula (I), the compound is shown in the specification,
Figure 347588DEST_PATH_IMAGE003
are all the control coefficients of the electric motor,
Figure 693119DEST_PATH_IMAGE004
the weight coefficients are controlled for the astigmatism distribution,
Figure 922106DEST_PATH_IMAGE005
is a weighting factor for the power accuracy,
Figure 720297DEST_PATH_IMAGE006
in the power distribution coefficient, x and y are coordinates of sample points, a is a minute area, and dA represents integration for the minute area.
S2, surface shape description equation
For the progressive surface (which may be the front surface or the back surface of the lens), the following surface description equation is proposed:
Figure DEST_PATH_IMAGE069
in the formula (I), the compound is shown in the specification,
Figure 60143DEST_PATH_IMAGE011
、
Figure 260180DEST_PATH_IMAGE012
、
Figure 660069DEST_PATH_IMAGE013
、
Figure 211136DEST_PATH_IMAGE014
、
Figure 354672DEST_PATH_IMAGE015
、
Figure 674795DEST_PATH_IMAGE016
all are the coefficients to be solved of the surface shape description equation.
For the profile rise equationzAssume definition
Figure 245585DEST_PATH_IMAGE017
、
Figure 18369DEST_PATH_IMAGE017
、
Figure 293492DEST_PATH_IMAGE018
、
Figure 77909DEST_PATH_IMAGE019
、
Figure 209813DEST_PATH_IMAGE020
The distribution is first and second partial differential in x, y directions, then, from the free-form surface equation, the mean curvature and gaussian curvature of each sample point can be known:
Figure 345259DEST_PATH_IMAGE022
Figure 220811DEST_PATH_IMAGE070
in the formula (I), the compound is shown in the specification,
Figure 874382DEST_PATH_IMAGE025
、
Figure 177188DEST_PATH_IMAGE025
、
Figure 534351DEST_PATH_IMAGE026
、
Figure 948015DEST_PATH_IMAGE027
、
Figure 707023DEST_PATH_IMAGE028
first and second partial differentials in the x and y directions, respectively;
Figure 383992DEST_PATH_IMAGE029
is an intermediate variable, and
Figure 353085DEST_PATH_IMAGE030
。
therefore, solving the minimum value problem of the evaluation function can be converted into a problem of how to adjust the undetermined coefficients so that the sum of the evaluation values of the evaluation functions of all the sample points is minimum, which is a typical least square solution problem.
S3, optimization process
Suppose that the 6 coefficients to be solved for the aspherical surface are each
Figure 445806DEST_PATH_IMAGE031
、
Figure 183955DEST_PATH_IMAGE032
、
Figure 703929DEST_PATH_IMAGE033
、
Figure 160318DEST_PATH_IMAGE034
、
Figure 56730DEST_PATH_IMAGE035
、
Figure 649386DEST_PATH_IMAGE036
Thus, the merit function at each sample point may be expressed by the following formula:
Figure 340261DEST_PATH_IMAGE038
in the formula (I), the compound is shown in the specification,
Figure 283946DEST_PATH_IMAGE039
the weighting factors are controlled for the astigmatism distribution of the ith sample point on the lens,
Figure 718470DEST_PATH_IMAGE040
is the mean curvature of the ith sample point on the lens,
Figure 431211DEST_PATH_IMAGE041
is the gaussian curvature of the ith sample point on the lens,
Figure 620884DEST_PATH_IMAGE042
is a weighting factor for the power accuracy of the ith sample point on the lens,
Figure 658722DEST_PATH_IMAGE043
is the power target value for the ith sample point on the lens,
Figure 755991DEST_PATH_IMAGE044
as a merit function for the ith sample point on the lens,
Figure 729764DEST_PATH_IMAGE045
namely, it is
Figure 887076DEST_PATH_IMAGE046
，
Figure 415140DEST_PATH_IMAGE047
Namely equivalent to
Figure 519362DEST_PATH_IMAGE041
，
Figure 206695DEST_PATH_IMAGE048
Namely equivalent to
Figure 410275DEST_PATH_IMAGE049
，
Figure 550269DEST_PATH_IMAGE050
Namely equivalent to
Figure 864707DEST_PATH_IMAGE040
，
Figure 406547DEST_PATH_IMAGE051
Namely equivalent to
Figure 781027DEST_PATH_IMAGE043
；
Thus, a matrix a can be defined whose elements are respectively:
Figure 408318DEST_PATH_IMAGE053
in the formula (I), the compound is shown in the specification,
Figure 526447DEST_PATH_IMAGE054
in order to be a differential sign, the sign of the differential,
Figure 188372DEST_PATH_IMAGE055
in order to evaluate the function of the measurement,
Figure 733754DEST_PATH_IMAGE056
is an independent variable;
then, using the classical least squares formulation, one can obtain:
Figure DEST_PATH_IMAGE071
in the formula (I), the compound is shown in the specification,
Figure 582761DEST_PATH_IMAGE059
is a coefficient matrix from x1 to x6,
Figure 507511DEST_PATH_IMAGE060
a transposed matrix representing the coefficient matrix a,pwhich represents the damping coefficient of the magnetic field,Irepresents a matrix of units, and represents a matrix of units,
Figure 758363DEST_PATH_IMAGE061
indicating the initial values before optimization. Presetting an initial value of aspheric coefficient
Figure 740226DEST_PATH_IMAGE062
Later, the corresponding can be calculated
Figure 342109DEST_PATH_IMAGE061
，
Figure 802040DEST_PATH_IMAGE065
。
Finally, the optimized aspheric surface coefficient is obtained by the following formula
Figure 376241DEST_PATH_IMAGE063
，
Figure 388059DEST_PATH_IMAGE064
。
The method comprises the steps of taking uniformly distributed discretization points on a lens as sample points, constructing an evaluation function by combining control coefficients, and finding the optimal coefficient solution of a surface shape description equation by using a least square method for the evaluation function so as to enable the sum of the evaluation functions of all the sample points to be minimum.
The invention firstly provides a surface shape description formula,
Figure DEST_PATH_IMAGE073
where the aspheric coefficients are to be evaluated in the present invention.
The discretization points which are uniformly distributed on the lens are taken as sample points, and the average curvature and the Gaussian curvature of each sample point can be described by a surface shape calculation formula:
Figure DEST_PATH_IMAGE075
Figure DEST_PATH_IMAGE077
control coefficient for each sample point
Figure 821446DEST_PATH_IMAGE078
、
Figure DEST_PATH_IMAGE079
And
Figure 616226DEST_PATH_IMAGE080
the distribution area of the maximum astigmatism can be finally controlled by adjusting the magnitude of these coefficients for preset adjustment parameters.
Thus, an evaluation function can be constructed
Figure 717037DEST_PATH_IMAGE082
Thereby obtaining a coefficient matrix
Figure DEST_PATH_IMAGE083
Then, by using a classical least square formula, an aspheric coefficient matrix X can be obtained
Figure 571861DEST_PATH_IMAGE084
。
Example 1
The asymptotic mirror of the present embodiment is designed as follows: the forward curve is spherical +1.82D, the luminosity of the far zone is-3.00, the luminosity of the near zone is-1.00, the added light is +2.00, and the refractive index of the lens is 1.55. The specific design method is as follows:
1) The power profile, astigmatism weight profile and power weight profile of the design lens are shown in fig. 2. The circular dashed area in fig. 2 is the lens size and the two arcs divide the entire distribution into 1 central area and 2 peripheral areas. The three weight distributions are respectively seen in 3 contour graphs and data tables corresponding to the three graphs. Wherein, the power distribution is shown in figure 3, and the distribution data is shown in table 1; the astigmatism weight distribution is shown in fig. 4, and the distribution data is shown in table 2; the power weight distribution is shown in fig. 5, and the data of the distribution is shown in table 3.
TABLE 1 target Power Profile data (power map)
Figure DEST_PATH_IMAGE085
TABLE 2 target alpha coefficient distribution data (alpha map)
Y\X -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0
40 54 54 54 54 54 54 54 54 54 54 54
36 54 54 54 54 54 54 54 54 54 54 54
32 54 54 54 54 54 54 54 54 54 54 54
28 54 54 54 54 54 54 54 54 54 54 54
24 54 54 54 54 54 54 54 54 54 54 54
20 54 54 54 54 54 54 54 54 54 54 54
16 54 54 54 54 54 54 54 54 54 54 54
12 35 54 54 54 54 54 54 54 54 54 54
8 30 31 35 54 54 54 54 54 54 54 54
4 30 30 30 31 33 37 42 54 54 54 54
0 30 30 30 30 30 30 31 32 35 54 54
-4 30 30 30 30 30 30 30 30 30 31 30
-8 30 30 30 30 30 30 30 30 30 30 30
-12 30 30 30 30 30 30 30 30 30 30 30
-16 30 30 30 30 30 30 30 30 30 30 30
-20 30 30 30 30 30 30 30 30 30 30 30
-24 30 30 30 30 30 30 30 30 30 30 30
-28 30 30 30 30 30 30 30 30 30 30 30
-32 30 30 30 30 30 30 30 30 30 30 30
-36 30 30 30 30 30 30 30 30 30 30 30
-40 30 30 30 30 30 30 30 30 30 30 30
Y\X 4 8 12 16 20 24 28 32 36 40
40 54 54 54 54 54 54 54 54 54 54
36 54 54 54 54 54 54 54 54 54 54
32 54 54 54 54 54 54 54 54 54 54
28 54 54 54 54 54 54 54 54 54 54
24 54 54 54 54 54 54 54 54 54 54
20 54 54 54 54 54 54 54 54 54 54
16 54 54 54 54 54 54 54 54 54 33
12 54 54 54 54 54 54 54 40 32 30
8 54 54 54 54 54 41 34 31 30 30
4 54 54 54 38 33 31 30 30 30 30
0 54 36 32 30 30 30 30 30 30 30
-4 31 30 30 30 30 30 30 30 30 30
-8 30 30 30 30 30 30 30 30 30 30
-12 30 30 30 30 30 30 30 30 30 30
-16 30 30 30 30 30 30 30 30 30 30
-20 30 30 30 30 30 30 30 30 30 30
-24 30 30 30 30 30 30 30 30 30 30
-28 30 30 30 30 30 30 30 30 30 30
-32 30 30 30 30 30 30 30 30 30 30
-36 30 30 30 30 30 30 30 30 30 30
-40 30 30 30 30 30 30 30 30 30 30
TABLE 3 target beta coefficient distribution data (beta map)
Y\X -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0
40 54 54 54 54 54 54 54 54 54 54 54
36 54 54 54 54 54 54 54 54 54 54 54
32 54 54 54 54 54 54 54 54 54 54 54
28 54 54 54 54 54 54 54 54 54 54 54
24 54 54 54 54 54 54 54 54 54 54 54
20 54 54 54 54 54 54 54 54 54 54 54
16 54 54 54 54 54 54 54 54 54 54 54
12 35 54 54 54 54 54 54 54 54 54 54
8 30 31 35 54 54 54 54 54 54 54 54
4 30 30 30 31 33 37 42 54 54 54 54
0 30 30 30 30 30 30 31 32 35 54 54
-4 30 30 30 30 30 30 30 30 30 31 30
-8 30 30 30 30 30 30 30 30 30 30 30
-12 30 30 30 30 30 30 30 30 30 30 30
-16 30 30 30 30 30 30 30 30 30 30 30
-20 30 30 30 30 30 30 30 30 30 30 30
-24 30 30 30 30 30 30 30 30 30 30 30
-28 30 30 30 30 30 30 30 30 30 30 30
-32 30 30 30 30 30 30 30 30 30 30 30
-36 30 30 30 30 30 30 30 30 30 30 30
-40 30 30 30 30 30 30 30 30 30 30 30
Y\X 4 8 12 16 20 24 28 32 36 40
40 54 54 54 54 54 54 54 54 54 54
36 54 54 54 54 54 54 54 54 54 54
32 54 54 54 54 54 54 54 54 54 54
28 54 54 54 54 54 54 54 54 54 54
24 54 54 54 54 54 54 54 54 54 54
20 54 54 54 54 54 54 54 54 54 54
16 54 54 54 54 54 54 54 54 54 33
12 54 54 54 54 54 54 54 40 32 30
8 54 54 54 54 54 41 34 31 30 30
4 54 54 54 38 33 31 30 30 30 30
0 54 36 32 30 30 30 30 30 30 30
-4 31 30 30 30 30 30 30 30 30 30
-8 30 30 30 30 30 30 30 30 30 30
-12 30 30 30 30 30 30 30 30 30 30
-16 30 30 30 30 30 30 30 30 30 30
-20 30 30 30 30 30 30 30 30 30 30
-24 30 30 30 30 30 30 30 30 30 30
-28 30 30 30 30 30 30 30 30 30 30
-32 30 30 30 30 30 30 30 30 30 30
-36 30 30 30 30 30 30 30 30 30 30
-40 30 30 30 30 30 30 30 30 30 30
2) Optimizing aspheric coefficients to minimize evaluation function
Assume that any given initial aspheric coefficients are:
Figure 617177DEST_PATH_IMAGE086
、
Figure DEST_PATH_IMAGE087
、
Figure 619244DEST_PATH_IMAGE088
、
Figure DEST_PATH_IMAGE089
、
Figure 699195DEST_PATH_IMAGE090
、
Figure DEST_PATH_IMAGE091
= [-100,0,-100,0,0,0]
according to the method and the calculation steps of the invention, the obtained aspheric coefficients are respectively as follows:
Figure 724920DEST_PATH_IMAGE092
、
Figure DEST_PATH_IMAGE093
、
Figure 929637DEST_PATH_IMAGE094
、
Figure DEST_PATH_IMAGE095
、
Figure 269482DEST_PATH_IMAGE096
、
Figure DEST_PATH_IMAGE097
= [-78.555，-1.303，-87.589， 1.344，0.0034，0.0028]
then, based on the calculated aspheric surface coefficients, substituting the aspheric surface description formula,
Figure DEST_PATH_IMAGE099
a curved surface is generated and the corresponding optical effects, such as astigmatism contour plots and spherical light contour plots, are shown in fig. 6 and 7.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (6)

1. A method for designing a progressive mirror capable of conveniently adjusting a maximum astigmatism distribution area, comprising the steps of:
s1, establishing an evaluation function related to focal power accuracy and astigmatism minimization;
s2, providing a set of surface shape description equations containing a plurality of unknown coefficients;
and S3, uniformly distributed discretization points on the lens are used as sample points, an evaluation function is constructed by combining control coefficients, and the optimal coefficient solution of the surface shape description equation is found by using a least square method for the evaluation function, so that the sum of the evaluation functions of all the sample points is minimum.
2. A method for designing a progressive lens to facilitate adjustment of the maximum astigmatism distribution area as claimed in claim 1, wherein the merit function is as follows:
Figure DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,
Figure 857293DEST_PATH_IMAGE002
are all the control coefficients of the electric motor,
Figure 829928DEST_PATH_IMAGE003
the weight coefficients are controlled for the astigmatism distribution,
Figure 397175DEST_PATH_IMAGE004
is a weighting factor for the power accuracy,
Figure 429854DEST_PATH_IMAGE005
in order to be the power distribution coefficient,His the mean curvature of the sample points and
Figure 348131DEST_PATH_IMAGE006
，Kis a Gaussian curvature of a sample point and
Figure 858878DEST_PATH_IMAGE007
，k 1 、k 2 the curvature is the principal curvature of the sample point, x and y are the coordinates of the sample point respectively, and A is the tiny area.
3. A method for designing a progressive mirror to facilitate adjustment of the maximum astigmatism distribution area according to claim 2, wherein the surface profile description equation is as follows:
Figure 546211DEST_PATH_IMAGE008
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE009
、
Figure 484211DEST_PATH_IMAGE010
、
Figure 624206DEST_PATH_IMAGE011
、
Figure 204223DEST_PATH_IMAGE012
、
Figure 746062DEST_PATH_IMAGE013
、
Figure 120543DEST_PATH_IMAGE014
all are coefficients to be solved of surface shape description equations.
4. A method for designing a progressive mirror for facilitating adjustment of maximum astigmatism distribution area as recited in claim 3, wherein in said step S3, the sagittal equation of the surface shape is usedzSuppose to define
Figure 419937DEST_PATH_IMAGE015
、
Figure 397121DEST_PATH_IMAGE015
、
Figure 262309DEST_PATH_IMAGE016
、
Figure 804761DEST_PATH_IMAGE017
、
Figure 919347DEST_PATH_IMAGE018
The distribution is first and second partial differential in x, y directions, then, from the free-form surface equation, the mean curvature and gaussian curvature of each sample point can be known:
Figure 575588DEST_PATH_IMAGE019
Figure 764124DEST_PATH_IMAGE020
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE021
、
Figure 11565DEST_PATH_IMAGE021
、
Figure 816710DEST_PATH_IMAGE022
、
Figure DEST_PATH_IMAGE023
、
Figure 604538DEST_PATH_IMAGE024
first and second partial differentials in the x and y directions, respectively;
Figure 850842DEST_PATH_IMAGE025
is an intermediate variable, and
Figure 862661DEST_PATH_IMAGE026
。
5. a method for designing a progressive mirror with convenient adjustment of maximum astigmatism distribution area as claimed in claim 4, wherein in said step 3, the assumed 6 coefficients to be obtained for the aspheric surface are respectively
Figure 561626DEST_PATH_IMAGE027
、
Figure 949883DEST_PATH_IMAGE028
、
Figure 50694DEST_PATH_IMAGE029
、
Figure 233413DEST_PATH_IMAGE030
、
Figure 13151DEST_PATH_IMAGE031
、
Figure 614552DEST_PATH_IMAGE032
Then the merit function at each sample point may be expressed using the following formula:
Figure 897766DEST_PATH_IMAGE033
in the formula (I), the compound is shown in the specification,
Figure 392332DEST_PATH_IMAGE034
the weighting coefficients are controlled for the astigmatism distribution of the ith sample point on the lens,
Figure 190524DEST_PATH_IMAGE035
is the mean curvature of the ith sample point on the lens,
Figure 530369DEST_PATH_IMAGE036
is the gaussian curvature of the ith sample point on the lens,
Figure DEST_PATH_IMAGE037
is a weighting factor for the power accuracy of the ith sample point on the lens,
Figure 668090DEST_PATH_IMAGE038
is the power target value for the ith sample point on the lens,
Figure 333557DEST_PATH_IMAGE039
an evaluation function for the ith sample point on the lens;
defining a matrix A, the elements of which are:
Figure 353466DEST_PATH_IMAGE040
in the formula (I), the compound is shown in the specification,
Figure 762582DEST_PATH_IMAGE041
in order to be a differential sign, the sign of the differential,
Figure 817125DEST_PATH_IMAGE042
in order to evaluate the function of the measurement,
Figure 387915DEST_PATH_IMAGE043
is an independent variable;
then, using the classical least squares formulation, one can obtain:
Figure 160699DEST_PATH_IMAGE044
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE045
is a coefficient matrix from x1 to x6,
Figure 904664DEST_PATH_IMAGE046
a transposed matrix representing the coefficient matrix a,pwhich represents the damping coefficient of the magnetic field,Irepresents a matrix of the unit cells,
Figure 420572DEST_PATH_IMAGE047
representing an initial value before optimization;
presetting an initial value of aspheric coefficient to
Figure 552476DEST_PATH_IMAGE048
Obtaining the optimized aspherical surface coefficient by the following formula
Figure 219080DEST_PATH_IMAGE049
，
Figure 969999DEST_PATH_IMAGE050
。
6. A method as claimed in claim 5, wherein in step 3, an initial value of aspheric coefficients is preset
Figure 999134DEST_PATH_IMAGE048
Calculating an initial value of the evaluation function by the following formula
Figure 911727DEST_PATH_IMAGE047
，
Figure 659103DEST_PATH_IMAGE051
。
CN202210440279.XA 2022-04-25 2022-04-25 Design method of progressive mirror capable of conveniently adjusting maximum astigmatism distribution area Pending CN115202069A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2024012183A1 (en) * 2022-07-12 2024-01-18 苏州派视光学有限公司 Sampling-point-adaptive gradually-changed focal power lens design method and lens

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2024012183A1 (en) * 2022-07-12 2024-01-18 苏州派视光学有限公司 Sampling-point-adaptive gradually-changed focal power lens design method and lens

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