CN115755430A - Free-form surface monofocal far-vision correction lens and design method - Google Patents
Free-form surface monofocal far-vision correction lens and design method Download PDFInfo
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Abstract
The application belongs to the field of ocular optics, and provides a free-form surface monofocal hyperopia correcting lens and a design method thereof, wherein the radial distance from each direction edge point of the hyperopia correcting lens to the center of a pupil is calculated; respectively calculating the vector height difference between the outer surface and the inner surface of the hyperopia correction lens in each direction by utilizing the diopter value of the hyperopia correction lens in each direction according to the monocular hypertoric prescription and the surface shape design parameters, and finding out the maximum vector height difference from the vector height difference, wherein the minimum center thickness of the hyperopia correction lens is equal to the maximum vector height difference plus the minimum edge thickness; adding the margin of edge cutting to the radial distance of each direction of the picture frame, checking and calculating the edge thickness before edge cutting in each direction, and if the minimum value of the edge thickness in each direction is greater than or equal to a set value, keeping the center thickness unchanged; and conversely, the edge thickness is set as a set value, and the center thickness is recalculated by combining the rise of the outer surface and the inner surface. This application lens center thickness and marginal thickness obviously reduce, have the light-duty beautiful thin effect of preferred.
Description
Technical Field
The invention belongs to the technical field of eye vision optics, and particularly relates to a lens for vision correction and a design method.
Background
In order to reduce the central thickness of the far-vision lens and achieve the purpose of reducing the weight of the lens, a vehicle room customized lens with the minimum edge thickness of 0.5mm before the edge cutting of a lens frame is usually adopted, a free-form surface is used on the inner surface of the lens, the central thickness is obtained by calculation in combination with an optometry prescription of a lens fitter, lens frame data, lens surface type data and the like, the lens is matched with the shape of the lens frame, and the central thickness of the lens is obviously reduced compared with the lens cast by a mold with the edge thickness not lower than 1.1mm and the diameter fixed to be 65mm or 70 mm. However, the edge thickness of the customized inner astigmatic zoom lens for the garage is calculated by adopting the diameter size containing the maximum radial size of the lens frame and the margin of the cutting edge, and the diameter size is positioned on the section of the inner surface base arc; according to the relation of the surface shape rise, the center thickness and the edge thickness, when the base arc is far away from the maximum radial dimension position of the spectacle frame, the calculated center thickness of the spectacle lens is obviously large, so that the edge thickness of the finished spectacle lens after edge cutting is large, the optimal effect of thinning the spectacle lens cannot be achieved, the weight of the spectacle lens is increased, and the wearing comfort is influenced.
Disclosure of Invention
In order to solve the problems proposed in the background art, the technical scheme of the invention is as follows:
a design method of a free-form surface monofocal hyperopic correction lens is provided, the hyperopic correction lens is a positive lens with an astigmatic correction surface on the inner surface, the inner surface is positioned at the eye using side, and the outer surface is arranged opposite to the inner surface; the outer surface is a spherical surface or an aspheric surface, and the inner surface is a toroidal curved surface; the design method comprises the following steps:
st1, firstly, calculating the radial distance from each directional edge point of the hyperopia corrective lens to the center of a pupil according to the independent pupillary distance and the pupil height of a single eye in the prescription of a spectacle dispenser, the selected coordinates of a spectacle frame and the width data of a nose bridge;
st2, calculating the rise difference between the outer surface and the inner surface of the hyperopic correction lens in each direction by using the diopter values of the hyperopic correction lens in each direction according to the prescription of the monocular super-toric surface and the surface shape design parameters, finding a maximum sagittal height difference from the sagittal height differences, the minimum central thickness of the hyperopic corrective lens being equal to the maximum sagittal height difference plus the minimum edge thickness; adding the margin of edge cutting to the radial distance of each direction of the picture frame, checking and calculating the edge thickness before edge cutting in each direction, and if the minimum value of the edge thickness in each direction is greater than or equal to a set value, keeping the center thickness unchanged; otherwise, the edge thickness is set, and the center thickness is recalculated by combining the rise of the outer surface and the inner surface;
st3, the center thickness obtained by the above method is used as a parameter to perform the vehicle room edging customization of the presbyopic lens.
Preferably, the frame coordinate data described in St1 includes: the shape, size and nose bridge width data of the inner frame; the method comprises the steps of obtaining through scanning a spectacle frame or obtaining through prestored coordinate data of the spectacle frame; the frame coordinate data is polar coordinate data (rho) of the edge point of the inner frame of the frame i ,θ i ) I =1 °,2 °, …,360 °; rho represents the distance from an edge point of the inner frame of the picture frame to a pole of a polar coordinate, and theta represents the angle of a ray of the edge point of the inner frame of the picture frame, which is connected with the pole, relative to a polar axis; the position of the polar coordinate pole is related to the placing precision of the mirror frame, and the pole position is arranged at the geometric center of the inner frame of the mirror frame, namely the intersection point of the half-height line and the half-width line of the inner frame of the mirror frame.
More specifically, the step of St1 calculating the radial distance from each directional edge point of the hyperopic corrective lens to the pupil center includes:
st1.1, polar coordinate data (ρ) of the selected rim point in the spectacle frame i ,θ i ) I =1 °,2 °, …,360 °, converted into rectangular coordinate data (X) i ,Y i ) I =1,2, …,360, where X i Abscissa value, Y, representing edge point i And expressing ordinate values representing the edge points, and converting the calculation formula as follows:
X i ＝ρ i cosθ i ，i＝1°,2°,…,360° (1)
Y i ＝ρ i sinθ i ，i＝1°,2°,…,360° (2)
st1.2, according to the independent pupil distance LPD of left eye or the independent pupil distance RPD of right eye, pupil height PH and the width DBL of the nose bridge of the selected frame type in the prescription of the prescription, the position (X) of the pupil center point on the frame type rectangular coordinate system is obtained 0 ，Y 0 ) The calculation formula is:
Y 0 ＝min(Y i )+PH，i＝1,2,…,360 (3)
left eye:
and (3) for the right eye:
in the formula, min (Y) i ) Means that the minimum value, max (X), is found from all the Y coordinate data of the rim points of the frame i ) Means finding the maximum value, min (X), from all X-coordinate data of the rim points of the frame i ) The minimum value is found from all X coordinate data of the edge points of the picture frame;
st1.3, finding out the radial distance rho from the edge point of each direction of the mirror frame to the center of the pupil i ；
According to the pupil center coordinates (X) 0 ，Y 0 ) The pupil center point position is translated to the origin of coordinates by translation, and the coordinates of the rim point of the mirror frame are changed to (N) xi ，N yi ) I =1,2, …,360; calculating the radial distance rho from the edge point of the picture frame to the center point of the pupil in each direction i I =1,2, …,360, the calculation formula is as follows:
N xi ＝X i -X 0 ，i＝1,2,…,360(6)
N yi ＝Y i -Y 0 ，i＝1,2,…,360(7)
more in detail, st2 determines the central thickness of the presbyopia correcting lens by the following steps:
st2.1, the prescription of the sphero-cylindrical lens of the lens dispenser is rewritten into a prescription in a negative internal astigmatism sheet form, after conversion, the outer surface of the lens is a spherical surface or an aspheric surface, and the inner surface is designed to be a toroidal curved surface;
st2.2 determining the refraction of the inner surface in all directions of the circumference according to the prescription of the negative internal dispersion tablet and the design requirement of the surface shape of the inner surfaceDegree F i (ii) a According to the negative internal astigmatism prescription and the refractive index of the lens, the curvature radius R1 of the outer surface of the lens is obtained;
st2.3, obtaining the radial distance rho from the edge point of the spectacle frame to the center of the pupil according to St1.3 i St2.2, outer surface spherical radius R1, and diopter F of inner surface in each direction i And calculating the outer surface rise S1 of the edge point of the picture frame in each direction according to the surface shape data of the inner surface i And inner surface rise S2 i From S1 according to the relation of the rise of the inner and outer surfaces, the edge thickness and the center thickness i -S2 i Find the maximum value in, plus the minimum edge thickness e min I.e. the minimum central thickness t of the presbyopia correcting lens min ；
t min ＝max(S1 i -S2 i )+e min ，i＝1,2,…,360
St2.4 radial distance ρ in each direction at edge point of lens i Plus the margin r of the cut edge 0 Checking and calculating the edge thickness e before edge cutting i Whether or not it satisfies the set value e or more 0 (ii) a If not, the center thickness needs to be increased to satisfy e i Is equal to e 0 (ii) a Increasing the radial distance from the edge point of the lens to the center of the pupil to ρ i +r 0 Recalculating rise of the inner and outer surfaces
And
then calculating the edge thickness e according to the relationship between the rise of the inner surface and the outer surface, the edge thickness and the center thickness i Finding out the minimum value; if the minimum value at this time is greater than or equal to e 0 Minimum center thickness t min The change is not changed; if the minimum value is less than e 0 Let e be the edge thickness in this direction (m direction) 0 Calculating the new central thickness of the lens
The calculation formula is as follows:
from e i Finding out the minimum value if the minimum value is greater than or equal to a set value e 0 Minimum center thickness t min The change is not changed; if the minimum value is less than the set value e 0 Let i = m at that position, then new center thickness
The calculation formula is as follows:
st3, using the minimum center thickness t obtained in St2 min Or
The car room edging of the presbyopic lens was performed as the center thickness of the presbyopic corrective lens.
Preferred r 0 ≤1.2mm，0.5mm≤e min ≤0.8mm，0.3mm≤e 0 ≤0.6mm。
The lens obtained by the method directly uses the radial size of the lens frame with the pupil center as the origin as the condition for calculating the edge thickness, calculates the rise of the inner surface and the outer surface by using the actual diopter value of each direction of the lens, finds out the rise difference generating the minimum edge thickness from the rise difference, and finally obtains the minimum center thickness. Compared with the comparative customized vehicle-room lens with the reduced lenses, the central thickness and the edge thickness of the lens are obviously reduced, and the maximum reduction of the lens thickness can be realized under the condition of meeting the requirement of the minimum edge thickness of the hyperopia correcting lens; in a similar way, the volume and the weight of the lens are reduced to a great extent compared with the original lens for shrinking, so that the finished lens has the best light and thin effects, and the comfort level of a wearer is increased.
When the monocular independent interpupillary distance, the nose bridge width, the spectacle frame data, the prescription and the surface shape parameters of a spectacle dispenser are determined, the position of the minimum edge thickness of the spectacle lens can be accurately found out to meet the technological requirements, and then the minimum center thickness of the spectacle lens is determined, so that the finished spectacle lens has the best light and thin effects.
The method for designing the free-form single-focus garage customized astigmatic lens for hyperopia correction is characterized in that the minimum edge thickness of the free-form lens obtained by the method is at or near the maximum radius of a lens frame with a pupil as the center, the radius of the frame with the pupil as the center is the main factor influencing the calculation of the center thickness, and the diopter of the inner surface and the outer surface of the lens in each direction is the second factor.
Drawings
FIG. 1 is a left rim shape of the eyeglasses;
FIG. 2 is a schematic view of the relative positions of the eye data and the frame;
FIG. 3 is an optical cross-sectional view of the conversion of the prescription of a sphero-cylindrical lens into a negative prescription of an internal negative astigmatism sheet according to one embodiment;
FIG. 4 is a schematic edge thickness comparison of finished lenses of the inventive and comparative lenses of example one;
FIG. 5 is a schematic representation of the location of minimum edge thickness for a lens of the invention and a comparative lens in one example;
FIG. 6 is a right frame shape of the eyeglasses;
FIG. 7 is a schematic comparison of edge thickness after edging of the inventive and comparative lenses of example two;
FIG. 8 is a schematic representation of the location of minimum edge thickness for the inventive and comparative lenses of example two.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below.
Example one
The prescription of the spherical cylindrical lens for the left eye of a lens dispenser is S +4.00D and C-2.00D, and the direction of the cylindrical lens is in the vertical direction of 90 degrees; the independent pupil distance LPD of the left eye of the lens dispenser is 33mm, the width DBL of the nose bridge is 18mm, and the pupil height PH is 22mm; the polar coordinate data of the edge points of the selected spectacle frame type are shown in table 1. The free-form surface monofocal far-vision correction lens for far-vision correction is designed according to the method of the invention, the central thickness of the lens is required to meet the requirement that the minimum edge thickness is 0.5mm after edge cutting, and the edge thickness is more than or equal to 0.3mm after the radial distance of each direction of the lens is added with 1mm edge cutting allowance; if the latter condition is not satisfied, the center thickness value may be increased appropriately so that the minimum value of the edge thickness in the latter case is 0.3mm.
The method comprises the following design steps:
st1, calculating the radial distance rho from each direction edge point of the hyperopia correction lens to the center of the pupil i ；
St1.1 polar coordinate data (ρ) of the rim point in the selected spectacle frame type shown in Table 1 i ，θ i ) I =1 °,2 °, …,360 °, converted into rectangular coordinate data (X) i ，Y i ) I =1,2, …,360; where ρ represents the distance from the rim point of the frame to the pole of the polar coordinate, and θ represents the angle of the ray connecting the pole with the rim point relative to the polar axis; in the embodiment, the default pole is positioned at the geometric center point of the spectacle frame; x i Abscissa value, Y, representing edge point i And (3) representing the ordinate values of the edge points, and converting the calculation formula as follows:
X i ＝ρ i cosθ i ，i＝1°,2°,…,360°
Y i ＝ρ i sinθ i ，i＝1°,2°,…,360°
drawing a frame type diagram from the above rectangular coordinate data, as shown in fig. 1, in which the position of X =0 and y =0 is the origin of the rectangular coordinate system;
st1.2, according to the independent pupil distance LPD of the left eye, the pupil height PH and the width DBL of the nose bridge of the selected frame type in the prescription of the prescription, the position (X) of the pupil center point of the frame type rectangular coordinate system is obtained 0 ，Y 0 ) The calculation formula is as follows:
Y 0 ＝min(Y i )+PH＝-21.24+22＝0.76mm，i＝1,2,…,360
left eye:
in the formula, min (Y) i ) Means finding the minimum, man (X), from all the Y-coordinate data of the rim points of the frame i ) The maximum value is found from all X coordinate data of the edge points of the picture frame; FIG. 2 is a schematic view of eye data and a frame position;
st1.3, finding out the radial distance rho from the edge point of each direction of the mirror frame to the center of the pupil i . By the pupil center point (X) 0 ，Y 0 ) Calculating rectangular coordinates (N) of frame edge points for the origin of coordinates xi ，N yi ) Then calculating the radial distance rho from the edge point of the picture frame to the center point of the pupil in each direction i I =1,2, …,360, the calculation formula is as follows:
N xi ＝X i -X 0 ，i＝1,2,…,360
N yi ＝Y i -Y 0 ，i＝1,2,…,360
wherein N is xi An abscissa value representing an edge point of the mirror frame after coordinate translation; n is a radical of yi And the vertical coordinate value of the edge point of the mirror frame after coordinate translation is represented.
From the radial distance ρ for facilitating subsequent comparison i Find out the maximum value rho max ：
ρ max ＝max(ρ i )＝29.76mm，i＝1,2,…,360
ρ max Plus the margin of edge cutting r 0 (= 1 mm) is the maximum radius r before the lens cut edge max ：
r max ＝ρ max +1＝30.76mm
St2, determining the center thickness t of the presbyopia correcting lens min ；
St2.1, changing the prescription of the sphero-cylindrical lens of the dispenser into a prescription in the form of negative internal dispersion; after conversion, the outer surface of the lens is designed to be spherical, and diopter is set to be +5.00DS; the inner surface is a toroidal curved surface, the base arc axial direction is 180 degrees, the shape is a high-order aspheric curve, the diopter is-1.00 DC, the orthogonal arc axial direction is 90 degrees, the shape is a parabola, the diopter is-3.00 DC, and the lens prescription of the converted negative inner scattering sheet is as follows:
the upper conversion is represented by an optical cross diagram, as shown in fig. 3, the left side of the middle number in the diagram is the original prescription of the cylindrical lens, and the right side is the prescription of the lens in the form of a negative internal dispersion sheet;
st2.2 calculating the dioptric power F of the inner surface of the presbyopia correcting lens in each circumferential direction i And the spherical radius R1 of the outer surface of the lens.
In this example, the diopter scale from the base curve to the orthogonal curve on the inner surface of the lens is designed to vary continuously, and the absolute value of the diopter scale in each direction is defined by the polar radius r of the next ellipse in polar coordinates i Represents; the minor axis semi-axis length of the ellipse is the absolute value of base arc diopter (-1.00 DC) (i.e. a = 1), the major axis semi-axis length of the ellipse is the absolute value of orthogonal arc diopter (-3.00 DC) (i.e. b = 3), the minor axis direction of the ellipse is located in the diopter direction of the base arc (gamma =90 deg.), and the distance r from each point to the pole on the ellipse i (polar diameter) represents the absolute value of diopter in each direction, and the diopter F in each direction of the circumference of the inner surface of the lens is obtained by adding a minus sign i The calculation formula is as follows:
substituting the parameters to obtain
The spherical radius R1 of the outer surface is determined from the refractive power (F1 = +5.00 DS) of the spherical surface of the outer surface and the refractive index (n = 1.56) of the material of the lens, and the calculation formula is as follows:
st2.3, determining the minimum central thickness t of the presbyopia correcting lens min (ii) a The radial distance rho from the edge point of the spectacle frame to the center of the pupil is obtained according to St1.3 i St2.2, the radius R1 of the outer surface sphere and the diopter F of the inner surface in each direction i And calculating the rise S1 of the outer surface of the edge point of the mirror frame in each direction according to the surface shape data of the inner surface i And inner surface rise S2 i From S1, based on the relationship between rise of inner and outer surfaces, edge thickness and center thickness i -S2 i Find the maximum value in, plus the minimum edge thickness e min (= 0.5 mm), i.e. the minimum central thickness t of the presbyopia correcting lens min (ii) a Here, it can also be understood as being from S2 i -S1 i Find the minimum value, plus the minimum center thickness t min I.e. minimum edge thickness e min (＝0.5mm)；
The outer surface rise calculation formula is:
the inner surface rise calculation is:
wherein k is a conic coefficient, a j Are high-order aspheric coefficients. In this example, k =0,a 2 ＝5.20e-07，a 3 = 5e-11, and the remaining coefficients are 0. c. C i The curvature of the apex of the curve in each direction of the circumference, c i ＝1/R i ，R i The calculation formula is as follows:
in the formula, F i The diopter of the lens inner surface in each direction was obtained for St2.2.
According to the mirrorThe relationship between the rise of the inner and outer surfaces of the sheet, the thickness of the edges and the thickness of the center is S1 i -S2 i Find the maximum value in, plus the minimum edge thickness e min I.e. the minimum central thickness t of the presbyopia correcting lens min The calculation formula is as follows:
t min ＝max(S1 i -S2 i )+e min ，i＝1,2,…,360
according to the calculation, S1 i -S2 i The maximum value of (a) occurs in the radial dimension of the frame, p max I =161, and
max(S1 i -S2 i )＝2.46mm
plus e min Value (= 0.5 mm), i.e. minimum edge thickness e min Radial dimension of rho appearing on the frame max In a position of
t min ＝max(S1 i -S2 i )+0.5＝2.46+0.5＝2.96mm
St2.4 radial distance ρ in each direction at edge point of lens i Plus the margin r of the cut edge 0 (= 1 mm), the edge thickness e before edge cutting is checked i Whether or not it satisfies the set value e or more 0 (= 0.3 mm); if not, the center thickness needs to be increased to satisfy e i Is equal to 0.3mm. Increasing the radial distance from the edge point of the lens to the center of the pupil to ρ i +1, recalculating rise of inner and outer surfaces
And
then calculating the edge thickness e according to the relationship between the rise of the inner surface and the outer surface, the edge thickness and the center thickness i Finding out the minimum value; if e i Is greater than or equal to 0.3mm, the minimum central thickness t min The change is not changed; if e i Is less than 0.3mm, e can be i The edge thickness of the position (i = m) where the minimum value of (c) is located is set to 0.3mm, and the new lens center thickness is calculated
The calculation formula is as follows:
the outer surface rise calculation formula is:
the inner surface rise calculation formula is:
the edge thickness calculation formula is:
from e i Finding out the minimum value if the minimum value is greater than or equal to a set value e 0 Minimum center thickness t min And is not changed. If the minimum value is less than the set value e 0 Let i = m at that position, then new center thickness
The calculation formula is as follows:
example e i Is 0.37mm, is greater than e 0 (= 0.3 mm), then the minimum center thickness is unchanged, t min ＝2.96mm。
To illustrate the thinning effect of this patent, the case-customized reduced mirror lenses having the radial dimensions including the maximum radial dimension of the frame and the margin of the cut edge used in calculating the center thickness mentioned in the background are compared based on the same prescription, frame and face shape data.
Because the human eye data and the spectacle frame data are the same, the maximum half of the customized reduction spectacle lens of the vehicle houseThe maximum radius r before the edge cutting max Same, so lens diameter D =2 × r max ＝2*30.76＝61.52mm。
Since the prescription and face shape data are also the same as those used in the present invention, the rise S corresponding to the spherical surface of the outer surface is calculated 1 * Then, according to St2.2, R1 is 112mm; and r is max =30.76mm, then:
setting a minimum edge thickness e at the base curve of the inner surface of the lens min 0.5mm, and a diopter F according to the base curve b Obtaining the vertex curvature radius r of the high-order aspheric surface curve of the inner surface base arc by the refractive index n of the lens b Calculating the rise S corresponding to the base arc b * . The distance vision lens has a center thickness t based on the relationship of the lens vector height, edge thickness and center thickness * ＝S 1 * +e min -S b * The specific calculation is as follows:
wherein c is the apex curvature, c =1/r b =1/560; r is the radial distance of the lens, where r = r max =30.76mm; k is the conic coefficient, a i Are high-order aspheric coefficients. In this example, k =0,a 2 ＝5.20e-07，a 3 = 5e-11, and the remaining coefficients are 0.
t * ＝S 1 * +e min -S b * ＝3.54mm
Compared with the lens of the invention, the difference value of the center thickness of the lens with the reduced mirror is as follows:
t * -t min ＝0.58mm
therefore, compared with a telescopic lens with the diameter of 61.52mm and the minimum edge thickness of 0.5mm at the base curve of the inner surface of the lens before the edge cutting, the telescopic lens designed by the invention has the advantages that the central thickness is reduced by 0.58mm, the reduction ratio is 16.38%, and the central thickness is further reduced.
Fig. 4 is an outline diagram of a finished lens product with the center of the pupil as the origin, edge thicknesses of two lenses are marked on the diagram at an interval of 30 degrees, wherein an inner numerical value of the frame is the edge thickness of the lens of the invention, an outer numerical value of the frame is the edge thickness of the reduction lens for comparison, a leading-out mark is a position where the edge thickness of the finished lens is the minimum, and the upper and lower parts of a dimension line are the edge thickness values of the reduction lens and the lens of the invention respectively. It can be seen from the figure that the edge thickness of the inventive lens is much smaller than that of the comparative lens, and that the volume and weight of the inventive lens are both much smaller than those of the original presbyopia corrective lens, which greatly increases the comfort of the wearer. It should be noted that, because the frame shape and the surface shape data of the two lenses are completely the same, and only the center thicknesses are different, the difference between the edge thicknesses of the two lenses is equal to the difference between the center thicknesses, and the difference change shown in the figure is caused by the data rounding error.
FIG. 5 shows the minimum edge thickness e of the inventive and comparative reduction lenses in calculating center thickness min The position of (a). As can be seen from the figure, e of the present invention min At the position of maximum radial dimension of the frame, i.e. p max C of reduction lens for comparison min Then on a circle of diameter D corresponding to the base curve of the inner surface of the lens, D =2 × r max ＝2×(ρ max +1). When the base arc position of the inner surface is just at the maximum radial dimension position rho of the lens frame max In the invention, the radial size of the lens is smaller than that of a reduction lens by only one cutting edge margin, the smaller radial size brings smaller vector height difference of the inner surface and the outer surface of the lens, and the finally obtained central thickness and edge thickness are also smaller, but the difference between the central thickness and the edge thickness is not too much; but when the base arc position of the inner surface is away from the maximum radial dimension position rho of the lens frame max Further away, such as the base arc position shown in FIG. 5 at 90, the maximum radial dimension ρ max In the 161 ° direction (i = 161), where there are not only the radial dimensions but also the variation in the rise of the vector due to the difference in power in each direction, which affects the center thickness and the edge thickness, the difference in the results of the two methods is relatively large. The circle corresponding to the base curve in this example is at a greater radial distance from the frame if the minimum edge thickness e is determined on a circle of this diameter D min (= 0.5 mm), according to the characteristic that the central thick edge of the far vision mirror is thin, the thickness of the minimum edge of the mirror frame where the base arc is located after the edge is cut is increased more than 0.5mm, as can be seen from figure 4, the thickness is increased by nearly five times when the thickness is increased from 0.5 to 2.91, and the thickness position of the minimum edge of the mirror frame is in rho max And not at the rim where the base curve is located, which means that the position where the base curve is again produced as the minimum edge thickness is not optimal. The best method is that the radial size of the spectacle frame taking the pupil center as the origin is directly used as the condition for calculating the edge thickness, the vector height of the inner surface and the outer surface is calculated by the actual diopter value of each direction of the lens, the vector height difference generating the minimum edge thickness is found out, and finally the minimum center thickness t is obtained min . The invention is designed and calculated based on the thought, so that the minimum edge thickness of the finished lens is equal to the minimum value which can be realized in the process, and the finished lens has the best light and thin effects.
Example two
The prescription of the sphero-cylindrical lens of the eye of a lens dispenser is S +3.50D, C-1.50D, and the direction of the cylindrical lens is in the oblique direction of 160 degrees; the independent interpupillary distance LPD of the right eye of the lens dispenser is 34mm, the width DBL of a nose bridge is 18mm, and the height PH of the pupil is 22mm; the polar coordinate data of the inner edge point of the selected spectacle frame type is shown in table 2. The free-form surface monofocal far-vision correction lens for far-vision correction is designed according to the method of the invention, the central thickness of the lens is required to meet the requirement that the minimum edge thickness is 0.5mm after edge cutting, and the edge thickness is more than or equal to 0.3mm after the radial distance of each direction of the lens is added with 1mm edge cutting allowance; if the latter condition is not satisfied, the center thickness value may be increased appropriately so that the minimum value of the edge thickness in the latter case is 0.3mm.
The method comprises the following design steps:
st1, calculating the radial distance ρ from each directional edge point of the hyperopia corrective lens to the center of the pupil i ；
St1.1, polar coordinate data (ρ) of the rim point in the selected spectacle frame type shown in Table 2 i ，θ i ) I =1 °,2 °, …,360 °, converted to rectangular coordinate data (X) i ，Y i ) I =1,2, …,360; the conversion calculation is as follows:
X i ＝ρ i cosθ i ，i＝1°,2°,…,360°
Y i ＝ρ i sinθ i ，i＝1°,2°,…,360°
drawing a frame type graph according to the rectangular coordinate data, as shown in FIG. 5;
st1.2, according to the independent interpupillary distance RPD of the right eye, the pupil height PH and the width DBL of the nose bridge of the selected frame type in the prescription of the prescription, the position (X) of the pupil center point of the frame type on the rectangular coordinate system of the frame type is obtained 0 ，Y 0 ) The calculation formula is as follows:
Y 0 ＝min(Y i )+PH＝-21.23+22＝0.77mm，i＝1,2,…,360
and (3) for the right eye:
in the formula, min (X) i ) The minimum value is found from all X coordinate data of the edge points of the picture frame; FIG. 2 is a schematic view of eye data and a frame position;
st1.3, finding the radial distance rho from each edge point of the frame to the center of the pupil i (ii) a The method is the same as the first embodiment;
also for facilitating subsequent comparisons, from the radial distance ρ i Find out the maximum value rho max ：
ρ max ＝max(ρ i )＝28.94mm，i＝1,2,…,360
ρ max Plus the margin r of the cut edge 0 (= 1 mm) is the maximum radius r before the lens cut edge max ：
r max ＝ρ max +1＝29.94mm
St2, determining the minimum center thickness t of a presbyopic corrective lens min ；
St2.1, changing the prescription of the sphero-cylindrical lens of the dispenser into a prescription in the form of negative internal dispersion; after conversion, the outer surface of the lens is designed to be spherical, and diopter is set to be +4.00DS; the inner surface is a toroidal curved surface, the axial direction of a base arc is 70 degrees, the shape is a high-order aspheric curve, and the diopter is-1.00 DC; the orthogonal arc is 160 degrees in axial direction, parabolic in shape, diopter of-2.00 DC, and the lens prescription of the converted negative internal astigmatism piece is as follows:
st2.2 calculating the dioptric power F of the inner surface of the presbyopia correcting lens in each circumferential direction i And the spherical radius R1 of the outer surface of the lens;
the method for determining diopter of each direction on the circumference of the inner surface of the lens is the same as that of the first embodiment, and the absolute value of diopter of each direction is the polar diameter r of the next ellipse in polar coordinates i And (4) showing. The minor axis length of the ellipse is the absolute value of base arc diopter (-0.5 DC) (i.e. a = 0.5), the major axis length of the ellipse is the absolute value of orthogonal arc diopter (-2.00 DC) (i.e. b = 3), the minor axis direction of the ellipse is located in the diopter direction of the base arc (gamma = 160), and the distance r from each point on the ellipse to the pole point i (polar diameter) represents the absolute value of diopter in each direction, and the diopter F in each direction of the circumference of the inner surface of the lens is obtained by adding a minus sign i The calculation formula is as follows:
substituting the parameters to obtain
Diopter (F) from the outer surface sphere 1 = 4.00 DS) and the refractive index of the material of the lens (n = 1.56), the spherical radius R1 of the outer surface is determined, and the calculation is performedThe following were used:
st2.3, determining the minimum central thickness t of the presbyopia correcting lens min . The method is the same as example one, and is calculated as follows:
the outer surface rise calculation formula is:
the inner surface rise calculation is:
wherein k =0,a 2 ＝5.20e-07，a 3 = 5e-11, and the remaining coefficients are 0. c. C i ＝1/R i ，R i The calculation formula is as follows:
according to the relation of the rise of the inner surface and the outer surface of the lens, the edge thickness and the center thickness from S1 i -S2 i The maximum value is found in (1), and the minimum edge thickness is added to 0.5mm, namely the minimum central thickness t of the far vision correction lens min The calculation formula is as follows:
t min ＝max(S1 i -S2 i )+0.5，i＝1,2,…,360
according to the calculation, S1 i -S2 i The maximum value of (a) occurs in the radial dimension of the frame, p max I =22, and
max(S1 i -S2 i ) =2.00mm, hence t min ＝2.50mm
St2.4 radial distance ρ in each direction at edge point of lens i Plus the margin of edge cutting r 0 (＝1mm)，Checking and calculating the edge thickness e before edge cutting i Whether or not 0.3mm or more is satisfied; if not, the center thickness needs to be increased to satisfy e i Is equal to 0.3mm. The method is the same as the example one, and the calculation formula is as follows:
the outer surface rise calculation formula is:
the inner surface rise calculation is:
the edge thickness calculation formula is:
example e i Is 0.39mm, is greater than 0.3mm, the minimum center thickness is unchanged, t min ＝2.50mm。
To illustrate the thinning effect of this patent, the far vision correcting lenses mentioned in the background of the invention, in which the radial dimensions used in calculating the center thickness include the maximum radial dimension of the frame and the margin of the cut edge, are compared, according to the same prescription, frame and face shape data.
Because the human eye data and the spectacle frame data are the same, the maximum radius r of the customized reduction spectacle lens for the vehicle house max Maximum radius r before edge cutting max Same, so lens diameter D =2 × r max ＝2×29.94＝59.88mm。
Since the prescription and the face shape data are also the same as those used in the present invention, the rise S corresponding to the spherical surface of the outer surface is calculated 1 * Then, according to St2.2, R1 is 140mm; r is max =29.94mm, the calculation formula is as follows:
setting a minimum edge thickness e at the base curve of the inner surface of the lens min 0.5mm, and F diopters according to the base curve b And the refractive index n of the lens is used for obtaining the vertex curvature radius r of the base arc of the high-order aspheric surface curve of the inner surface b Calculating the rise S corresponding to the base arc b * . The distance vision lens has a center thickness t according to the relationship of the lens vector height, edge thickness and center thickness * ＝S 1 * +e min -S b * . The specific calculation is as follows:
wherein c is the apex curvature, c =1/r b =1/1120; r is the radial distance of the lens, where r = r max =29.94mm; k is the conic coefficient, a i Are high-order aspheric coefficients. In this example, k =0,a 2 ＝5.20e-07，a 3 = 5e-11, and the remaining coefficients are 0.
t * ＝S 1 * +e min -S b * ＝2.96mm
Compared with the lens of the invention, the difference value of the center thickness of the lens with the reduced mirror is as follows:
t * -t min ＝2.96-2.50＝0.46mm
therefore, compared with the telescopic lens with the diameter of 59.88mm and the minimum edge thickness of 0.5mm at the base curve of the inner surface of the lens before the cutting edge, the central thickness of the telescopic lens designed by the invention is reduced by 0.46mm, the reduction ratio is 15.54 percent, and the central thickness is further reduced.
Fig. 6 is a profile view of a finished spectacle frame with the center of the pupil as the origin, and as in fig. 4 of the first example, the edge thicknesses of the finished spectacle lenses of the two designs are marked at intervals of 30 °, and the position and size where the edge thicknesses of the two spectacle lenses are the minimum are marked on the drawing. It can be seen from the figure that the edge thickness of the inventive lens is much smaller than that of the comparative lens, and that the volume and weight of the inventive lens are both much smaller than those of the original presbyopia corrective lens, which greatly increases the comfort of the wearer.
FIG. 7 shows the minimum edge thickness e of the inventive and comparative reduction lenses in calculating the center thickness in example two min The position of (a). As can be seen from the figure, e of the present invention min (= 0.5 mm) at the maximum radial dimension position of the rim, i.e. p max At (i = 22), and e of the comparative reduction lens min (= 0.5 mm) is on the circle with diameter D corresponding to the base arc of the inner surface of the lens, D =2 xr max ＝2×(ρ max + 1) having a difference in the margin of the cutting edge in the radial dimension, and also having a difference in the rise of the inner and outer surfaces due to the difference in position, resulting in an actual minimum edge thickness at the maximum radial position of the frame defined in the present invention, i.e. ρ max To (3). Therefore, the method of the invention can accurately find the position of the minimum edge thickness of the lens according to the requirements of the lens dispenser such as the independent pupil distance of the single eye, the width of the nose bridge, the data of the spectacle frame, the prescription, the surface shape parameters and the like, so that the position meets the process requirements, and further the minimum center thickness of the lens is determined, so that the finished lens has the best light and thin effects.
TABLE 1 polar coordinate data table of inner edge points of selected eyeglass frame type in the first embodiment
TABLE 2 polar coordinate data table of inner edge points of selected eyeglass frame type in example two
Claims (6)
1. A design method of a free-form surface monofocal hyperopic correction lens is provided, the hyperopic correction lens is a positive lens with an astigmatic correction surface on the inner surface, the inner surface is positioned at the eye using side, and the outer surface is arranged opposite to the inner surface; the outer surface is a spherical surface or an aspheric surface, and the inner surface is a toroidal curved surface; the design method is characterized by comprising the following steps:
st1, firstly, calculating the radial distance from each direction edge point of the hyperopia correcting lens to the center of a pupil according to the independent pupil distance and the pupil height of a single eye in the prescription of the spectacle wearer, the coordinate of the selected spectacle frame and the width data of a nose bridge;
st2, calculating the vector height difference between the outer surface and the inner surface of the hyperopic correction lens in each direction by utilizing the diopter values of the hyperopic correction lens in each direction according to the monocular super-toroidal surface prescription and the surface shape design parameters, and finding out the maximum vector height difference from the vector height difference, wherein the minimum central thickness of the hyperopic correction lens is equal to the maximum vector height difference plus the minimum edge thickness; adding the margin of edge cutting to the radial distance of each direction of the picture frame, checking and calculating the edge thickness before edge cutting in each direction, and if the minimum value of the edge thickness in each direction is greater than or equal to a set value, keeping the center thickness unchanged; otherwise, the edge thickness is set, and the center thickness is recalculated by combining the rise of the outer surface and the inner surface;
st3, vehicle room edging and prescription of presbyopic lenses are performed using the center thickness obtained by the above method as a parameter.
2. The method of designing a free-form, monofocal presbyopic corrective lens of claim 1, characterized by: the picture frame inside casing data mirror include: the frame coordinate data described in St1 includes: the shape, size and nose bridge width data of the inner frame; the method comprises the steps of obtaining through scanning a spectacle frame or obtaining through prestored coordinate data of the spectacle frame; the frame coordinate data is polar coordinate data (rho) of the edge point of the inner frame of the frame i ，θ i ) I =1 °,2 °, …,360 °; rho represents the distance from an edge point of the inner frame of the picture frame to a polar coordinate pole, and theta represents the angle of a ray of the edge point connecting the pole in the inner frame of the picture frame relative to a polar axis; the position of the polar coordinate pole is related to the placing precision of the mirror bracket, and the pole position is arranged at the geometric center of the inner frame of the mirror frame, namely the intersection of the half-height line and the half-width line of the inner frame of the mirror frame.
3. The method for designing a free-form, monofocal presbyopia corrective lens of claim 1 wherein St1 calculates the radial distance from each directional edge point of the hyperopic corrective lens to the center of the pupil comprising:
st1.1, polar coordinate data (ρ) of the selected rim point in the spectacle frame i ，θ i ) I =1 °,2 °, …,360 °, converted to rectangular coordinate data (X) i ，Y i ) I =1,2, …,360, where X i Abscissa value, Y, representing edge point i And expressing ordinate values representing the edge points, and converting the calculation formula as follows:
X i ＝ρ i cosθ i ，i＝1°,2°,…,360° (1)
Y i ＝ρ i sinθ i ，i＝1°,2°,…,360° (2)
st1.2, according to the independent pupil distance LPD of left eye or the independent pupil distance RPD of right eye, the pupil height PH in the prescription of the spectacle dispenser, and the width DBL of the nose bridge of the selected frame type, the position (X) of the pupil center point on the frame type rectangular coordinate system is obtained 0 ，Y 0 ) The calculation formula is:
Y 0 ＝min(Y i )+PH，i＝1,2,…,360 (3)
left eye:
and (3) for the right eye:
in the formula, min (Y) i ) Means that the minimum value, max (X), is found from all the Y coordinate data of the rim points of the frame i ) Means finding the maximum value, min (X), from all X-coordinate data of the rim points of the frame i ) The minimum value is found from all X coordinate data of the edge points of the picture frame;
st1.3, finding out the radial distance rho from the edge point of each direction of the mirror frame to the center of the pupil i ；
According to the pupil center coordinates (X) 0 ，Y 0 ) The pupil center point position is translated to the origin of coordinates by translation, and the coordinates of the rim point of the mirror frame are changed to (N) xi ，N yi ) I =1,2, …,360; calculating the radial distance rho from the edge point of the picture frame to the center point of the pupil in each direction i I =1,2, …,360, the calculation formula is as follows:
N xi ＝X i -X 0 ，i＝1,2,…,360 (6)
N yi ＝Y i -Y 0 ，i＝1,2,…,360 (7)
4. the method of designing a free-form, monofocal presbyopic corrective lens of claim 1 wherein St2 determines the center thickness of the presbyopic corrective lens comprising the steps of:
st2.1, the prescription of the sphero-cylindrical lens of the lens dispenser is rewritten into a prescription in a negative internal astigmatism sheet form, after conversion, the outer surface of the lens is a spherical surface or an aspheric surface, and the inner surface is designed to be a toroidal curved surface;
st2.2, determining the diopter F of the inner surface in each circumferential direction according to the prescription of the negative internal scattering film and the surface shape design requirement of the inner surface i (ii) a According to the negative internal astigmatism prescription and the refractive index of the lens, the curvature radius R1 of the outer surface of the lens is obtained;
st2.3, obtaining the radial distance rho from the edge point of the spectacle frame to the center of the pupil according to St1.3 i St2.2, outer surface spherical radius R1, and diopter F of inner surface in each direction i And calculating the rise S1 of the outer surface of the edge point of the picture frame in each direction according to the surface shape data of the inner surface i And inner surface rise S2 i From S1, based on the relationship between rise of inner and outer surfaces, edge thickness and center thickness i -S2 i Find the maximum value in, plus the minimum edge thickness e min I.e. the minimum central thickness t of the presbyopia correcting lens min ；
t min ＝max(S1 i -S2 i )+e min ，i＝1,2,…,360
St2.4 radial distance ρ in each direction at edge point of lens i Plus the margin of edge cutting r 0 Checking and calculating the edge thickness e before edge cutting i Whether or not it satisfies the set value e or more 0 (ii) a If not, the center thickness is increased to satisfy e i Is equal to e 0 . Increasing the radial distance from the edge point of the lens to the center of the pupil to ρ i +r 0 Recalculating rise of the inner and outer surfaces
And
then, according to the relation between the rise of the inner surface and the outer surface, the edge thickness and the center thickness, the edge thickness e is calculated i Finding out the minimum value; if the minimum value at this time is greater than or equal to e 0 Minimum center thickness t min The change is not changed; if the minimum value is less than e 0 Let e be the edge thickness in this direction (m direction) 0 Calculating the new central thickness of the lens
The calculation formula is as follows:
from e i Finding out the minimum value if the minimum value is greater than or equal to a set value e 0 Minimum center thickness t min Keeping the original shape; if the minimum value is less than the set value e 0 Let i = m at that position, then new center thickness
The calculation formula is as follows:
st3, using the minimum center thickness t obtained in St2 min Or
The car room edging of the presbyopic lens was performed as the center thickness of the presbyopic corrective lens.
5. The method of designing a free-form, monofocal presbyopic corrective lens of claim 4, characterized in that: r is 0 ≤1.2mm，0.5mm≤e min ≤0.8mm，0.3mm≤e 0 ≤0.6mm。
6. A free-form, unifocal, presbyopic corrective lens, comprising: obtained using the method of designing a free-form, monofocal distance correcting lens according to any one of claims 1 to 5.
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