CN113655634B - Lens capable of reducing side-center defocusing and design method thereof - Google Patents
Lens capable of reducing side-center defocusing and design method thereof Download PDFInfo
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- CN113655634B CN113655634B CN202110998298.XA CN202110998298A CN113655634B CN 113655634 B CN113655634 B CN 113655634B CN 202110998298 A CN202110998298 A CN 202110998298A CN 113655634 B CN113655634 B CN 113655634B
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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
- G02C7/06—Lenses; Lens systems ; Methods of designing lenses bifocal; multifocal ; progressive
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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
Abstract
The invention relates to a lens for reducing decentration and a design method thereof. One refraction surface of the spectacle lens is a design surface which is designed by a free-form surface and reduces the lateral center defocusing, and the focal power change rates of a transverse meridian and a longitudinal meridian are respectively controlled by adopting a high-order polynomial to obtain the focal power distribution on the design surface; and then according to the refractive index of the lens, obtaining the curvature radius of each point of the design surface and the curvature center position corresponding to the curvature radius, thereby calculating the rise of the design surface. According to the technical scheme, the focal power change gradient of the off-focus area of the design surface is reduced, the speed of astigmatism increase of the off-focus area is reduced, the larger astigmatism caused by the non-Tornike design of the ellipse is balanced, the correction effect of the hyperopic defocus compensation can be effectively improved, and the wearing comfort of teenagers is improved.
Description
Technical Field
The invention relates to an eyeglass, in particular to an eyeglass capable of reducing side-center defocusing and a design method thereof, and particularly relates to an eyeglass suitable for teenagers to inhibit myopia deepening.
Background
Along with the rapid development of modern society science and technology, display screen equipment is more and more, when enriching people's life, also lead to people to use the eye excessively, teenagers are at near-sighted formation in-process, peripheral eyesight is in out of focus, the state such as blur around the sight point, cause the field of vision to contract, thereby cause teenagers' hypermetropic defocus, lead to near-sighted deepening, wear and reduce other central hypermetropic out-of-focus lens, lens periphery adopts out-of-focus design, make retina peripheral object image be near-sighted out-of-focus state, thereby restrain the visual axis and increase, restrain near-sighted deepening.
The horizontal visual range of people is wide and the longitudinal visual range is wide, so in most cases, the visual requirements of people for the left and right are higher than the visual requirements for the upper and lower parts, therefore, in the side-center out-of-focus design, different out-of-focus compensation designs are adopted for two directions, and the variation of the focal power of the left and right parts of the lens is slower than that of the upper and lower parts. Chinese utility model patent CN210136372U discloses a lens that adopts the other center out of focus design of reduction of the oval distribution of dioptric profile, the horizontal astigmatism of the lens of design in 20mm semi-bore department accounts for 92% that the average focal power changes, vertical astigmatism in 20mm semi-bore department accounts for 110% that the average focal power changes, because oval non-torquer design, the proportion of the vertical astigmatism of lens for average focal power offset value is obviously higher than horizontal for the vertical astigmatism of lens is bigger than the design of rotational symmetry. There are studies showing that: the astigmatism existing in the periphery of the spectacle lens is a main factor causing discomfort in wearing, and therefore, the spectacle lens of the out-of-focus design with reduced elliptical distribution reduces wearing comfort and reduces the correcting effect of hyperopic out-of-focus.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the lens capable of reducing the side-center defocus and the design method thereof, wherein the correction effect of the hyperopic defocus compensation can be effectively improved, and the wearing comfort level is improved.
The technical scheme for realizing the aim of the invention is to provide a design method for reducing the off-center out-of-focus spectacle lens, wherein one refraction surface of the spectacle lens is a design surface for reducing the off-center out-of-focus, and the design steps of the design surface are as follows:
(1) Constructing a Cartesian coordinate system by taking the center of the design surface of the lens as an origin, wherein the positive direction of a y axis is the transverse meridian direction of the design surface to the right, the positive direction of an x axis is the longitudinal meridian direction of the design surface to the down, and the positive direction of a z axis is perpendicular to the paper surface to the outside; central focal power of lens obtained according to optometry resultD 0 Taking the value of the focal power at the edge of the lens minus the focal power at the center of the lens as the defocus compensation value of the lensADDAnd u is the distance from the center of the design surface in the longitudinal meridian direction of the design surface, and a power variation curve D (u) at u is obtained according to formula (I):
wherein the content of the first and second substances,A n for higher order coefficients, the following system of equations is usedObtaining:
wherein R is the radius of the lens, d is the radius value of the lens in the longitudinal meridian direction of the design surface, d is more than or equal to 18 and less than or equal to 22 mm, 0<k<0.5；
(2) Obtaining a power distribution D (x, y) on the design surface according to formula (II):
wherein w is the longitudinal meridian directionxIn the direction of the transverse meridianyPower ratio of 0<w<1；
(3) According to the refractive index of the lens, the curvature radius r (x, y) of each point of the design surface and the curvature center position corresponding to the curvature radius are obtained through calculation, and then the rise z (x, y) of the design surface is obtained through calculation.
The invention relates to a design method for reducing a decentered spectacle lens, which has the following preferable scheme: 0.15 ≤k≤0.45；0.55≤w≤0.95。
The technical scheme of the invention also comprises the spectacle lens for reducing the decentration by the design method.
The invention provides a spectacle lens capable of reducing the decentration defocusing, wherein the focal power on the surface of the spectacle lens is distributed in a concentric elliptical ring shape.
The other refraction surface of the lens is one of a spherical surface, a diffusing surface, a double-smooth surface, a progressive multi-focus surface and a multi-point defocusing structural surface.
When the distance between the eyes is 12 mm and the eyes are at a viewing field angle of 30 degrees, the defocus compensation values of the transverse meridian and the longitudinal meridian of the spectacle lens are respectively 0.80D-2.5D and 0.90D-3.00D.
The technical scheme of the invention is based on the principle that: it is known from Minkwitz's theorem (see document: esser G, becken W, altheimer H, et al. General theory of the Minkwitz the objective to non-nuclear threads of systematic surfaces [ J ]. Journal of the Optical Society of America A, 2017, 34 (3): 441.), and the rate of change of astigmatism in the transverse meridian direction y of the lens is proportional to the rate of change of power in the longitudinal meridian direction x, as shown in equation (1):
wherein C is lens astigmatism; d is the focal power of the lens.
As can be seen from equation (1), the power change rate at a distance u = d from the center of the design surface in the longitudinal meridian direction of the design surface is reducedkThus, the larger astigmatism due to the elliptical non-etock design can be reduced, as shown by the following equation (2):
wherein u is the distance from the center of the design surface in the longitudinal meridian direction of the design surface, and when u = d, the coefficient of the higher order term of the power distribution curve in the meridian of the lens in the vertical directionA 1 , A 2 , A 3 , A 4 , A 5 Can be calculated by the following augmented matrix (3):
wherein R is the radius of the lens, and d is a certain radius value of the lens in the longitudinal meridian direction of the design surface.
The power distribution curve in the longitudinal meridian direction can be obtained from the high-order polynomial coefficient according to equation (4)D(u)：
The design surface is concentric with the upper part of the circular ring transverselyA longitudinal power ratio ofw，0<w<Power profile of the entire surface of the lensD(x, y) Is obtained as shown in the following formula (5):
the radius of curvature distribution of the lens surface is formula (6):
wherein n is the refractive index of the lens.
According to the technical scheme disclosed in the united states patent document US5123725, the curvature center coordinates corresponding to the curvature radius of each point on the surface of the lens are calculated, and the curvature center coordinates (ξ, η,
) As in equation (7):
wherein:
from the radius of curvature of the lensrAnd corresponding center coordinates of curvature (ξ, η,
) The rise of the lens surface is calculated according to equation (8): />
Compared with the prior art, the invention has the beneficial effects that: according to the method, the focal power change gradient of the design surface defocusing area is reduced by adopting a method of controlling the focal power change rate of the lens by a high-order polynomial, so that the speed of increasing astigmatism of the defocusing area is reduced, the aim of reducing larger astigmatism caused by the non-Tornike design of elliptical defocusing is fulfilled, the correction effect of far-vision defocusing compensation can be effectively improved, and the wearing comfort level is improved.
Drawings
FIG. 1 is a schematic diagram of a structure for reducing the power distribution of the surface of a decentered spectacle lens according to example 1 of the present invention;
FIGS. 2 and 3 are graphs showing the variation of the power in the x-direction and the cylindrical power in the x-direction in the defocus design plane provided in example 1 of the present invention and in comparative example 1, respectively;
FIGS. 4 and 5 are graphs showing the variation of the power and the astigmatism in the transverse y-direction of the off-focus design plane provided in example 2 of the present invention and that of comparative example 2, respectively;
FIGS. 6 and 7 are graphs showing the power and astigmatism variation curves in the longitudinal direction x and the transverse direction y of the defocus design plane provided in example 3 of the present invention;
fig. 8 and 9 are graphs showing the power and astigmatism changes in the longitudinal x and transverse y directions, respectively, of the surface of a conventional lens scale 3 using an unoptimized design.
Detailed Description
The technical solution of the present invention is further explained with reference to the drawings and the embodiments.
Example one
In this embodiment, the radius R of the lens is 36 mm, the refractive index n of the lens is 1.56, and the corrective central power of the lens (the central power of the lens obtained as a result of the optometry)D 0 ) Defocus compensation from center to edge of the lens at-2.00D (power)ADDWas 2.00D. One refracting surface of the lens is a defocusing design surface and can be a front surface or a rear surface, and the other refracting surface of the lens is one of a spherical surface, a diffusing surface, a double-smooth surface, a progressive multi-focus surface and a multi-point defocusing structure surface.
The specific design method of the out-of-focus design surface of the lens is as follows:
a Cartesian coordinate system is constructed by taking the center of a design surface of the lens as an original point, the positive direction of a y axis is the horizontal meridian direction of the design surface to the right, the positive direction of an x axis is the vertical meridian direction of the design surface to the downward, and the positive direction of a z axis is perpendicular to the paper surface to the outward.
When a person wears the glasses, the semi-caliber of the used lens is about 20mm, so that the semi-caliber value d =20mm of the lens in the longitudinal meridian direction of the design surface, the power change gradient k at the 20mm caliber of the lens is controlled to be 0.255, u is the distance from the longitudinal meridian direction of the design surface to the center of the design surface, and the following steps are obtained:
the focal power of the lens at the maximum aperture is D 0 + ADD, yielding:
to ensure that the power change is gradual, the first derivative at the end of the power change curve is 0, resulting in:
to make the aberration in the out-of-focus zone smaller, the second derivative at the end of the out-of-focus zone of the lens is 0, resulting in:
five higher order coefficients can be solved from the above five equations, and in the present embodiment, the higher order coefficients of the power profile in the lens longitudinal meridian are shown in table 1:
TABLE 1
| Coefficient of performance | A 1 | A 2 | A 3 | A 4 | A 5 |
| Value of | -9.7578e-18 | -3.0218e-4 | 1.0252e-4 | -2.0193e-6 | 9.4335e-16 |
In the present embodiment, the power ratio of the transverse direction y to the longitudinal direction x of the concentric rings of the design surface isw，wThe value is 0.832.
According to the formula (4) Obtaining the focal power distribution curve in the longitudinal meridian directionD(u)。
The power distribution of the entire surface of the lens was calculated by the following equation (5)D(x, y)。
The curvature radius distribution r (C) of the lens surface is calculated according to the formula (6)x, y)。
According to the technical scheme disclosed in the patent document US5123725, the coordinates (xi, eta,
) In the formula, eachuAnd matching with a spherical surface formed by a corresponding curvature center and a corresponding curvature radius, wherein the enveloping surfaces of the series of spherical surfaces are the rise of the gradual change surface, and calculating the rise z (x, y) of the design surface according to a rise calculation formula (8).
Referring to fig. 1, it is a schematic diagram of the power distribution structure of the surface of the spectacle lens designed according to the technical solution of the present embodiment, and the powers are distributed in the shape of concentric elliptical rings.
The variation curve of the longitudinal focal power and the astigmatic power of the designed surface can be obtained by calculating the focal power distribution and the astigmatic distribution of the lens.
According to the requirements and parameters of the lens of the embodiment, the technical scheme disclosed in the Chinese utility model patent CN 207301528U is adopted, and the lens which is optimally designed by adopting the prior art and is not astigmatic is taken as a comparative example 1.
Referring to fig. 2 and 3, graphs of the variation of the focal power and the cylindrical power in the longitudinal x direction of the lens of the present embodiment and the lens of comparative example 1 are shown; as can be seen in fig. 3: under the condition that the longitudinal 20mm half-caliber defocus compensation value is 1.16D, the astigmatism value reaches 1.03D, and the astigmatism value is 88.8% of the defocus compensation value; in the embodiment of fig. 2, the optimization method is adopted for design, and under the condition that the longitudinal compensation values are the same, the astigmatism value is only 0.69D, and the astigmatism value is 59.5% of the defocus compensation value.
Example two
In this embodiment, the parameters of the lens to be designed are the same as those in the first embodiment, and the transverse dimension of the lens is 20mm and a halfThe caliber compensation value is the same as that of the first embodiment, the defocus compensation at the position of a longitudinal half caliber d =20mm is 80% of the transverse defocus compensation value, and the ratio of the transverse y to the longitudinal x focal power on the concentric ring of the defocus design surface iswThe value is 0.894.
Controlling the power change gradient k at the aperture of the lens d =20mm to be 0.185, yielding:
the focal power of the lens at the maximum caliber is D 0 + ADD, yielding:
to ensure that the power change is gradual, the first derivative at the end of the power change curve is 0, resulting in:
to make the aberration in the out-of-focus area smaller, the second derivative at the end of the out-of-focus area of the lens is 0, and we get:
five higher-order coefficients can be obtained by solving the above five equations, and the higher-order coefficients of the power distribution curve on the lens longitudinal meridian are shown in table 2:
TABLE 2
| Coefficient of performance | A 1 | A 2 | A 3 | A 4 | A 5 |
| Value of | -6.7588e-18 | -3.2438e-4 | 1.1558e-4 | -5.8336e-6 | 5.2468e-16 |
Calculating according to the formula (4) to obtain a focal power distribution curve in the longitudinal meridian directionD(u)。
The power distribution of the entire surface of the lens was calculated by the equation (5)D(x, y)。
The curvature radius distribution r (C) of the lens surface is calculated according to the formula (6)x, y)。
On-lens calculation according to formula (7)The coordinates of the center of curvature (ξ, η,
)。
the rise z (x, y) of the design surface is calculated according to the formula (8).
According to the requirements and parameters of the lens preparation of the embodiment, the technical scheme disclosed by the Chinese utility model patent CN210136372U is adopted, and the lens obtained by the same optimization design of astigmatism in two directions is adopted as the comparative example 2.
Referring to fig. 4 and 5, graphs of the variation of the transverse y-direction power and the astigmatism of the lens of the embodiment and the lens of the comparative example 2 are respectively provided; as can be seen from fig. 5: the astigmatism value at the transverse 20mm semi-caliber position is 70.7 percent of the defocus compensation value; as can be seen from fig. 4, with the design compensation method provided by this embodiment, the lateral astigmatism value is only 48.6% of the defocus compensation value.
EXAMPLE III
In this example, the lens radius R was 36 mm, the refractive index n was 1.56, and the corrective central sphere power of the lens (the central power of the lens obtained as a result of optometry)D 0 ) is-2.00D (focal power), the astigmatism of the lens is 1.50D, the axial direction of the astigmatism is in the 180-degree direction, the defocus compensation quantity ADD from the center to the edge of the lens is 2.00D, and the ratio of the transverse y to the longitudinal x optical power on a concentric ring of a defocus design surfacewIs 0.795.
Controlling the gradient k of the focal power change at the aperture of 20mm of the lens to be 0.384, and obtaining:
the focal power of the lens at the maximum aperture is D 0 + ADD, yielding:
to ensure that the power change is smooth, the first derivative at the end of the power change curve is 0, and the following results are obtained:
to make the aberration in the out-of-focus zone smaller, the second derivative at the end of the out-of-focus zone of the lens is 0, resulting in:
five higher-order coefficients can be obtained by the above five equations, and the higher-order coefficients of the power distribution curve on the lens longitudinal meridian are shown in table 3:
TABLE 3
| Coefficient of performance | A 1 | A 2 | A 3 | A 4 | A 5 |
| Value of | -6.8425e-18 | -5.2538e-4 | 3.1258e-4 | -7.1836e-6 | 5.8462e-16 |
Calculating according to the formula (4) to obtain a focal power distribution curve in the longitudinal meridian directionD(u)。
The power distribution of the entire surface of the lens was calculated by the following equation (5)D(x, y)。
The curvature radius distribution r (C) of the lens surface is calculated according to the formula (6)x, y)。
The coordinates (xi, eta,
)。
the rise z (x, y) of the design plane is calculated according to the formula (8).
Referring to fig. 6 and 7, the present embodiment provides graphs of the power of the defocus design plane in the longitudinal direction x and the transverse direction y, respectively, versus the cylindrical power. As can be seen from FIGS. 6 and 7, the technical solution of the present invention is adopted to perform the novel non-Tornike design compensation on the lens, and the astigmatism value of the lens at the 20mm half-aperture position in the transverse direction and the longitudinal direction is 0.92D.
According to the lens matching requirements and parameters of the embodiment, the technical scheme disclosed by the Chinese utility model patent CN 207301528U is adopted, the lens obtained by the unoptimized common design method is the comparative example 3, and the change curves of the surface longitudinal and transverse focal power and the astigmatism are respectively shown in figures 8 and 9; as can be seen from the figure: the astigmatism at 20mm half-diameter in the transverse direction and the longitudinal direction of the lens is 0.98D and 1.25D respectively.
Compared with the lens with the out-of-focus design adopted in the prior art, the lens provided by the embodiments 1, 2 and 3 of the invention adopts the novel non-Tornike design compensation method, and the focal power change gradient can be controlled by using a high-order polynomial, so that the larger astigmatism caused by the elliptical non-Tornike design is effectively balanced, the wearing comfort of teenagers is improved, and the myopia correction effect of the lens is also improved.
Claims (7)
1. A design method for reducing a side center out-of-focus spectacle lens is characterized in that one refracting surface of the spectacle lens is a side center out-of-focus reducing design surface, and the design steps of the design surface are as follows:
(1) Constructing a Cartesian coordinate system by taking the center of the design surface of the lens as an origin, wherein the positive direction of a y axis is the transverse meridian direction of the design surface to the right, the positive direction of an x axis is the longitudinal meridian direction of the design surface to the down, and the positive direction of a z axis is perpendicular to the paper surface to the outside; central focal power of lens obtained according to optometry resultD 0 The value obtained by subtracting the central focal power of the lens from the edge focal power of the lens is used as the defocus compensation value of the lensADDAnd u is the distance from the center of the design surface in the longitudinal meridian direction of the design surface, and a power variation curve D (u) at u is obtained according to formula (I):
wherein the content of the first and second substances,A n the coefficient of the high-order term is obtained according to the following equation:
wherein R is the radius of the lens, d is the radius value of the lens in the longitudinal meridian direction of the design surface, d is more than or equal to 18 and less than or equal to 22 mm,kfor the power change rate at a distance u = d from the center of the design surface in the longitudinal meridian direction of the design surface, 0<k<0.5；
(2) Obtaining a power distribution D (x, y) on the design surface according to formula (II):
wherein w is the longitudinal meridian directionxIn the direction of the transverse meridianyPower ratio of 0<w<1；
(3) According to the refractive index of the lens, the curvature radius r (x, y) of each point of the design surface and the curvature center position corresponding to the curvature radius are obtained through calculation, and then the rise z (x, y) of the design surface is obtained through calculation.
2. The design method for reducing the off-center out-of-focus spectacle lens as claimed in claim 1, wherein: 0.15 ≤k≤0.45。
3. The design method for reducing the off-center out-of-focus spectacle lens as claimed in claim 1, wherein: 0.65-0w≤0.95。
4. A spectacle lens for reducing side-center defocus obtained by the design method as claimed in claim 1.
5. The spectacle lens of claim 4, wherein: the focal power of the lens surface is distributed in a concentric elliptical ring shape.
6. The spectacle lens of claim 4, wherein: the other refracting surface of the lens is one of a spherical surface, a diffusing surface, a double-smooth surface, a progressive multi-focus surface and a multi-point defocusing structural surface.
7. The spectacle lens for reducing side-center defocus according to claim 4, wherein: the distance between the spectacle lenses is 12 mm, and the defocusing compensation values of the transverse meridian and the longitudinal meridian of the spectacle lens are respectively 0.80D-2.5D and 0.90D-3.00D at the visual field angle of 30 degrees.
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| US10901237B2 (en) * | 2018-01-22 | 2021-01-26 | Johnson & Johnson Vision Care, Inc. | Ophthalmic lens with an optically non-coaxial zone for myopia control |
| EP3598213A1 (en) * | 2018-07-20 | 2020-01-22 | Carl Zeiss Vision International GmbH | Varifocal spectacle lens with a spatially varying refractive index |
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