A method for regionally optimizing astigmatism in a progressive multifocal ophthalmic lens

Abstract

This invention relates to an optimization method for progressive multifocal lenses. First, a portion of the progressive multifocal lens surface is replaced by a linear superposition of that area and a spherical surface. The spherical surface used is the one whose boundary is closest to the boundary of the replaced lens area, calculated using the least squares method. Then, Zernike polynomials are used to selectively fit the surface elevation of the replaced lens, further smoothing the progressive multifocal lens surface. This invention can control the optical power and astigmatic distribution in the astigmatic region of the progressive multifocal lens surface by changing the location and range of the region, thereby improving surface astigmatism and helping wearers obtain a better visual experience.

Description

TECHNICAL FIELD

[0001] The present application relates to an optimization method of progressive multifocal ophthalmic lens, in particular to a method of regional optimization of astigmatism of progressive multifocal ophthalmic lens. BACKGROUND

[0002] Progressive multifocal ophthalmic lens has the characteristics of continuous change of optical power from top to bottom, which can meet the needs of the wearer for distance and near vision, and avoid the defects such as visual disruption of bifocal lenses when switching between distance and near vision. Its application in daily life is becoming more and more widespread. The surface of progressive multifocal ophthalmic lens is mainly divided into four regions (see the attached Figure 1 ), which are distance vision zone 1, near vision zone 2, intermediate transition zone (progressive channel) 3 and astigmatism zone 4. Distance vision zone 1 is located in the wide area of the upper half of the progressive multifocal ophthalmic lens, which provides a wide and clear field of view when the eye is in a relaxed and level state; near vision zone 2 is used to observe near objects, and the clear vision range is smaller than that of distance vision zone; distance vision zone 1 and near vision zone 2 are connected by intermediate transition zone (progressive channel) 3, which is used to observe objects between distance and near, and is the main feature of progressive multifocal lens distinguishing from bifocal lenses; astigmatism zone 4 generally cannot be used for observation, and is the area with lower visual acuity in the progressive multifocal ophthalmic lens; Figure 1 A is the reference point of distance vision zone, B is the reference point of near vision zone, and the specific position is different due to the different types of progressive multifocal ophthalmic lens, design methods, correction degree, eye pupil distance and eye habits, etc.

[0003] The far vision zone 1, the near vision zone 2 and the transition zone 3 of the progressive addition ophthalmic lens are collectively referred to as the effective vision zone, and the remaining area is the astigmatic zone 4, so that the effective vision zone area is relatively small, thereby affecting the clear vision range of the lens wearer. The surface of the initially designed progressive addition ophthalmic lens often meets the design requirements in most areas, but some areas still do not meet the design requirements, and modifying the initial design parameters will also make the optical properties of the more ideal area worse, so an optimization method is needed that does not change the optical properties and can improve the local optical defects. Reference 1 (Gao J D, Xiang H Z, Li N N, et al. Influence of weight function on the design of progressive addition ophthalmic lenses [J]. Chinese Journal of Lasers, 2020, 49(9): 0922001.) studies that setting a weight function in different areas of the lens surface can reduce the peripheral astigmatism; Reference 2 (Shen W M, Xue M Q. Aberration analysis and design of aspheric ophthalmic lenses [D]., 2002.) proposes that appropriately optimizing the shape factor of the lens can correct the lens aberration according to the Seidel primary aberration theory; Reference 3 (Lu H Y, Bai D F, Ma J W. Design of initial sag model of progressive addition lens surface [J]. Progress of Laser and Optoelectronics, 2017, 54(3): 032201.) proposes a progressive line as the initial sag model of the meridian line of the transition zone of the progressive addition ophthalmic lens, which lays a foundation for the later optimization design of the astigmatism of the progressive addition ophthalmic lens; Reference 4 (Li N N, Xiang H Z, Gao J D, et al. Design of aspheric ophthalmic lenses based on genetic algorithm [J]. Optics Instrument, 2021, 43(3): 36-44.) designs aspheric ophthalmic lenses by using a multi-objective optimization genetic algorithm to reduce the astigmatism of the lenses; the present application linearly superimposes the sag of the surface of the progressive addition ophthalmic lens in some areas and the sag of the spherical surface, and uses Zernike polynomials to selectively fit the replaced sag in some areas, so as to improve the astigmatism of the lens surface and help the lens wearer to obtain a better visual experience. SUMMARY

[0004] The present application aims to overcome the shortcomings of the prior art, and provides a method for regionally optimizing the astigmatism of a progressive addition ophthalmic lens based on the design method of the progressive addition ophthalmic lens, which can effectively reduce the peripheral astigmatism of the lens to improve the visual experience of the lens wearer.

[0005] The present application aims to provide a method for regionally optimizing the astigmatism of a progressive addition ophthalmic lens.(1) Select the optimization area, (2) find the sag of the spherical surface for replacing the above optimization area, (3) linearly superimpose the sag of the initial surface of the lens in the optimization area and the sag of the spherical surface obtained in step (2), (4) use Zernike polynomials to selectively fit the replaced sag, and (5) calculate the optimized surface shape sag using the Zernike polynomial coefficients obtained by fitting.

[0006] Minkwitz theorem shows that there is a positive correlation between the rate of increase of optical power on the meridian and the rate of increase of astigmatism in the perpendicular meridian direction, reference 5 (Barbero S, del Mar González M. Admissible surfaces in progressive addition lenses [J]. Optics Letters, 2020, 45(20): 5656-5659.) uses geodesic curvature and principal curvature to derive the astigmatism expression at non-meridian, and the two principal curvatures at any point on the sphere are equal, so the sphere has the feature of geometrically no astigmatism, and the use of spherical sag instead of initial sag can effectively reduce the surface astigmatism of progressive addition ophthalmic lenses in theory.

[0007] The sudden change of sag at the boundary of the optimization area will produce a large astigmatism, and the Zernike polynomial can play a certain smoothing effect while fitting the lens surface. For example, a random noise is added to the spherical surface, and the three-dimensional graph is shown in Figure 1. Figure 2 , 66 Zernike polynomials are used for fitting, and the three-dimensional graph of the fitting result is shown in Figure 2. Figure 3 , and Figure 3. Figure 2 and Figure 4. Figure 3 It can be seen that after Zernike polynomial fitting, high-frequency noise is filtered, low-frequency signals of the spherical surface are retained, and a smoothing effect is achieved.

[0008] The method for regionally optimizing astigmatism of a progressive addition ophthalmic lens provided by the application specifically includes but is not limited to the following steps:

[0009] 1. Select the optimization area:

[0010] The coordinate system is set as follows: the positive direction of the x-axis is vertically downward, the positive direction of the y-axis is horizontally to the right, and the positive direction of the z-axis is perpendicular to the paper and points to the reader. The length unit is mm. The distribution diagram of the optimization area of the lens surface is shown in Figure 5. Figure 4 The optimization area is set as a circle, and the center coordinates are (x1, y1), (x2, y2) and (x3, y3), and the radii are r1, r2 and r3, respectively, wherein -30 < y1 < 0, x1 > 0, 0 < y2 < 30, x2 > 0,

[0011] 0 < y3 < 30, 2 < r1 < 15, 2 < r2 < 15,

[0012] 2 < r3 < 15; the position and coverage range of the circular area are adjusted by controlling the center coordinates and radii.

[0013] 2. Find the spherical sag for replacing the above optimization area:

[0014] ① Set the spherical equation expression for replacing the lens surface:

[0015]

[0016] where i is the number of the optimization region, taking values 1, 2, 3, (ξ i , η i , ζ i ) are the spherical center coordinates, and R i is the spherical curvature radius.

[0017] ② Take the spherical center coordinates (ξ i , η i , ζ i ) and the curvature radius R i as unknown parameters, and construct a variance integral objective function of the distance between the spherical boundary and the optimization region boundary:

[0018]

[0019] where z0 is the initial surface sag of the lens, L is the boundary of the optimization region, and J i is the objective function.

[0020] ③ Use a numerical optimization method to search for the optimal center coordinates (ξ i , η i , ζ i ) and the curvature radius R i to minimize the value of formula (2). The numerical optimization method used includes but is not limited to the least square method.

[0021] 3. Linearly superimpose the initial surface sag in the optimization region of the lens and the sag of the spherical surface obtained in step 2, and the superimposed sag expression is as follows:

[0022] Z i = m i ·z i + n i ·z0, (3)

[0023] where z i is the linear superimposed sag, z0 is the initial sag of the lens, m i , n i are non-negative constants, and m i + n i = 1.

[0024] 4. Use Zernike polynomials to perform selective regional fitting on the replaced sag:

[0025] Zernike polynomials have the characteristics of continuity and orthogonality in the unit circle domain, and the coefficients of different polynomials are independent of each other, which is beneficial to eliminate the interference of accidental factors, and provides an effective method for selectively processing each aberration coefficient and optimizing system performance. Here, the Zernike polynomials in the polar coordinate system are used, and the expression is as follows:

[0026] Z nm (r, θ) = R nm (r)e imθ , (4)

[0027] In the formula, n = 0, 1, …, ∞; 0≤|m|≤n; n-|m| is an even number; R nm (r) is a real-valued radial polynomial; r is the normalized radius of a point on the lens, and θ is the polar angle of the point on the lens in the polar coordinate system.

[0028] The Zernike polynomials are used to replace the selective area fitting of the sag, and the area not participating in the fitting is marked as 0 in the Zernike polynomial fitting program, so as to not affect the Zernike polynomial coefficients after fitting. The area within a certain range at the boundary of the optimization area does not participate in the Zernike polynomial fitting, and the range of the area not participating in the fitting is limited as follows:

[0029] (b i r i ) 2 ≤(x-x i ) 2 +(y-y i ) 2 ≤(a i r i ) 2 , (5)

[0031] Wherein, i is the number of the optimization area, and the value is 1, 2, 3, a i , b i are constants and 0.8≤b i <1, 1<a i ≤1.2, which are used to adjust the range of the area not participating in the fitting.

[0032] 5. The fitted Zernike coefficients are substituted into the Zernike polynomials to calculate the optimized surface sag.

[0033] The obtained sag data is input into a numerical control milling and grinding machine tool to directly process the progressive surface on the inner or outer surface of a resin or glass lens, and then the progressive multi-focal ophthalmic lens is manufactured by polishing with the numerical control machine tool. The obtained sag data can also be processed into a glass mold or a metal mold by a free-form surface grinding method, which is used to manufacture the progressive multi-focal ophthalmic lens.

[0034] The progressive multi-focal ophthalmic lens optimization method has the beneficial effects that the regional spherical replacement can reduce the astigmatism of the progressive multi-focal ophthalmic lens without changing the optical performance outside the lens optimization region, and the Zernike polynomial fitting can further smooth the sag of the progressive multi-focal ophthalmic lens and reduce the astigmatism caused by the sudden change of the lens surface. The optimization method makes the optimization of the progressive multi-focal ophthalmic lens more flexible and convenient, effectively improves the optical performance of the near vision region and the astigmatism region, and enables the lens wearer to obtain a better visual experience. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The figure is a distribution diagram of four regions of a progressive multi-focal ophthalmic lens, 1 region is a distance vision region, 2 region is a near vision region, 3 region is an intermediate transition region (a gradual transition channel), and 4 region is an astigmatism region. Points A and B are a distance vision reference point and a near vision reference point, respectively.

[0036] Figure 2 The figure is a three-dimensional graph of the sag after adding random noise to the spherical surface.

[0037] Figure 3 The figure is a three-dimensional graph of the sag after fitting with 66 Zernike polynomials.

[0038] Figure 4 The figure is a distribution diagram of an optimization region.

[0039] Figure 5 The figure is a three-dimensional graph of the initial sag of the progressive multi-focal ophthalmic lens in Example 1.

[0040] Figure 6 The figure is a contour map of the initial optical power of the progressive multi-focal ophthalmic lens in Example 1.

[0041] Figure 7 The figure is a contour map of the initial astigmatism of the progressive multi-focal ophthalmic lens in Example 1.

[0042] Figure 8 The figure is a three-dimensional graph of the difference between the replaced sag and the initial sag of the progressive multi-focal ophthalmic lens in Example 1.

[0043] Figure 9 The figure is a three-dimensional graph of the sag of the progressive multi-focal ophthalmic lens in Example 1 after fitting with Zernike polynomials.

[0044] Figure 10Optimized power contour map of the progressive addition ophthalmic lens in Example 1.

[0045] Figure 11 Optimized astigmatism contour map of the progressive addition ophthalmic lens in Example 1. DETAILED DESCRIPTION

[0046] The technical solutions of the present application will be further described in combination with the drawings and examples:

[0047] Example

[0048] In this example, the initial sag of the progressive addition ophthalmic lens is shown in Fig. 1, and the initial power and astigmatism contour maps are shown in Figs. 2 and 3, respectively. Figure 5 The corresponding power and astigmatism contour maps are shown in Figs. 4 and 5, respectively. Figure 6 and 7 The radius R0 of the lens is 40 mm, the far vision zone power is 4.25 diopters, the near vision zone power is 6.00 diopters, the add power ADD is 1.75 diopters, and the refractive index of the lens material is 1.58.

[0049] The center coordinates of the optimization region 1 are set as (2, -7), and the region radius r1 is 8 mm; the center coordinates of the optimization region 2 are set as (7, 12), and the region radius r2 is 8 mm; the center coordinates of the optimization region 3 are set as (10, 2), and the region radius r3 is 6 mm.

[0050] The center coordinates of the replacement sphere in region 1 are obtained by least square search as (-3.2231, -0.3949, 113.3937), and the radius is 113.4487 mm; the center coordinates of the replacement sphere in region 2 are (-3.9752, 0.0908, 112.7125), and the radius is 112.8437 mm; the center coordinates of the replacement sphere in region 3 are (-1.3620, 0.2356, 96.8463), and the radius is 96.8473 mm. Substituting the above data into equation (1), the corresponding sag of the sphere is obtained.

[0051] The initial sag is linearly superimposed with the sag of the sphere in the lens surface regions 1, 2 and 3 according to equation (3), wherein m1 = m2 = 0.05, m1 = m2 = 0.05, m3 = 0.4, and n3 = 0.6. The initial sag is replaced by the superimposed sag in the three regions, and the difference between the front and back surfaces of the progressive addition ophthalmic lens before and after replacement is shown in Fig. 6. Figure 8 As can be seen from the figure, the sag at the boundary of the optimization region appears to be abrupt, which will produce a large astigmatism.

[0052] Smoothing is performed by Zernike polynomial fitting. The boundary of the three optimization regions is not involved in the fitting region, and is calculated according to equation (5), wherein b i = 0.95, and a i=1.05, i is the number of the region not participating in the fitting, and i=1, 2, 3. When the Zernike polynomial is used for fitting, the points at the boundaries of the above three optimized regions do not participate in the fitting, and the Zernike coefficients obtained by fitting are used to calculate the optimized surface height. See the attached Figure 9 .

[0053] The differential geometry method is used to calculate the power and astigmatism of the optimized progressive multifocal ophthalmic lens. The power and astigmatism contour maps of the optimized progressive multifocal ophthalmic lens in this embodiment are shown in the attached Figure 10 and 11 .

[0054] In Example 1, the astigmatism in the far vision zone and the near vision zone of the progressive multifocal ophthalmic lens before and after optimization is less than 0.25 diopters in the area without change. The comparison of the optical performance before and after optimization is shown in Table 1. As can be seen from Table 1, the power in the far vision zone and the near vision zone does not change before and after optimization, the astigmatism in the left astigmatism zone is reduced by 14.0 mm 2 , which is reduced by 87.5%, the astigmatism in the right astigmatism zone is reduced by 6.5 mm 2 , which is reduced by 12.7%; the maximum astigmatism of the lens before optimization is 2.00 diopters, and the maximum astigmatism of the lens after optimization is 1.75 diopters, which is reduced by 12.5%; the area of the near vision zone with astigmatism less than 0.06 diopters is increased from 12.0 mm 2 to 33.0 mm 2 , which is increased by 63.6%.

[0055] Table 1 Comparison of the optical performance before and after optimization of Example 1

[0056]

[0057]

[0058] The height data of the optimized progressive multifocal ophthalmic lens is input into a numerical control milling and grinding machine tool for processing, and the progressive multifocal ophthalmic lens is made after polishing by the numerical control machine tool.

[0059] The method for optimizing the astigmatism of the regions of the progressive multifocal ophthalmic lens according to the present application can significantly reduce the maximum astigmatism and the area of the large astigmatism region while keeping the power in the far vision zone and the near vision zone unchanged, and can significantly increase the area of the near vision zone with astigmatism less than 0.06 diopters, which helps to improve the visual experience of the lens wearer.

Claims

1. A method of regionally optimizing astigmatism for a progressive multifocal ophthalmic lens, characterized in that, The method comprises the following steps: (1) selecting an optimization area, (2) The optimal spherical curvature radius R is obtained by minimizing the objective function i and the spherical curvature center coordinates (ξ i , η i , ζ i ), the spherical sag is obtained according to the spherical equation, and the objective function is expressed as follows: wherein i is the number of the optimization area, taking values of 1, 2, 3, z0 is the initial sag of the lens, and L is the boundary of the optimization area, (3) linearly superimposing the initial surface sag in the optimization area of the lens and the spherical sag obtained in step (2), (4) performing selective area fitting on the replaced sag by using Zernike polynomials, wherein in the fitting process, the area within a certain range at the boundary of the optimization area does not participate in the Zernike polynomial fitting, and the area within a certain range at the boundary of the optimization area refers to an area satisfying the following inequality, (b i r i ) 2 ≤(x-x i ) 2 +(y-y i ) 2 ≤(a i r i ) 2 , where i is the number of the optimization region, taking values 1, 2, 3, x i and y i are the centers of the respective optimization regions, r i is the radius of the circular optimization region, a i , b i are constants and 0.8≤b i <1, 1≤a i ≤1.2, for adjusting the range of the regions not involved in the fitting, (5) calculating the optimized surface sag by using the fitted Zernike coefficients.

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