JP2021033036A - Interpolation method for interpolating optical performance of unknown area of progressive refractive power lens - Google Patents

Abstract

To provide an interpolation method for interpolating an optical performance of an unknown area of a progressive refractive power lens capable of constructing an appropriate surface shape about an area where optical performance data does not exist.SOLUTION: In a progressive refractive power lens having an area in which an optical performance is unknown (thereafter, an interpolation object lens), the present invention relates to an interpolation method for interpolating an optical performance of the area having the optical performance unknown, and the interpolation method is configured to: estimate a distribution function of the optical performance on the basis of optical performance data on the area having the optical performance known next to the area having the optical performance unknown as to a plurality of progressive refractive power lenses; and apply location information on the area having the optical performance of the interpolation object lens unknown to the distribution function to thereby calculate the optical performance of the area having the optical performance unknown.SELECTED DRAWING: Figure 6

Description

The present invention relates to an interpolation method for interpolating a region of unknown optical performance of a progressive power lens having a region of unknown optical performance.

The progressive power lens is an aspherical lens having two refractive power regions having different refractive powers and a progressive region in which the refractive power (power) changes progressively between the two regions. There is a peculiarity that the dioptric power of the distance portion is relatively negative and the dioptric power of the near portion is relatively positive. Therefore, for a lens having a negative power, when the negative power is strong, the luminous flux for measurement of the mapping device is greatly refracted, and the performance distribution around the distance portion may not be obtained. On the contrary, for a lens with a positive intensity number, the performance distribution in the near region may not be obtained. In addition, data may be lost on a part of the lens surface due to the influence of the mark engraved on the lens or the painted mark even in areas other than the peripheral area.
In addition, he wants to evaluate whether the performance of the progressive power lens manufactured in-house is within the specified range, or if there are multiple product variations, he wants to confirm that the lens has the selected design without mistake. There is a request. In addition, there is a request to investigate the performance of other companies' products and utilize them in the development of their own products. In such a case, a so-called mapping device is used in which a large number of luminous fluxes are transmitted through the lens and the optical performance distribution is measured based on the result of refraction of them. However, other companies' products are often available only with so-called lens-shaped lenses that have been processed to fit the frame, rather than circular lenses that are so-called round lenses before processing. Even if it is available as a round lens, the range in which the optical performance distribution can be accurately measured by the mapping device is larger than the general diameter size (φ70-80) of the round lens before it is processed into the shape of the frame. It is a narrow area (about φ50 to 60). In the present specification, for example, "φ70" indicates that the diameter is 70 mm.
Therefore, it may not be possible to obtain the optical performance distribution on the periphery of the round lens.
For these reasons, there has been a demand for obtaining an optical performance distribution in a wider range for a round lens of a progressive power lens.
Also, when investigating other companies' products, there is a request to make a prototype of a similar lens and compare it with a monitor, but even if the optical performance distribution is measured using a mapping device, the circumference of the round lens is the same as above. Since it may not be possible to measure, there was a request to obtain an optical performance distribution over a wider area as well.

Further, in the design of the progressive power lens, the optical distribution to be the target of the design can be definitively determined in the vicinity of the center of the progressive power lens, for example, in the region of about φ50. It is possible to get the result that the subject actually wears the monitor by fitting the actually prototype lens into the spectacle frame and "satisfied with the lens" or "it is good to improve in this way", and the result is This is because the optical performance can be determined based on the above.
On the other hand, it is difficult to obtain such findings in areas far from the center. However, it is customary for spectacle lens manufacturers to make round lenses (for example, φ70-80) that are large to some extent, and in order to deliver in that shape, we have set a design goal that extends the desired performance in the outer peripheral direction. Then you have to design the lens.
Further, when processing a round lens, it is necessary to consider the convenience of operation of a freeform processing machine for producing a lens of that size. During machining, the machining lines must be connected smoothly. For example, even with a round lens with a diameter of φ70 to 80, in order for the tool to move smoothly, the shape of the outer region, for example, φ100, should be smoothed. Need to be determined. Therefore, for example, there is a demand to create rational performance distribution data of at least φ70 to 80, more preferably about φ100, in a shorter time based on a narrow optical distribution near the center of about φ50.

Japanese Unexamined Patent Publication No. 2014-222315 Japanese Unexamined Patent Publication No. 2016-004178

As described above, there is no direct technique for constructing a valid surface shape in a region where optical performance data does not exist. For example, Patent Document 1 discloses a method in which a target optical performance is represented by a Zernike polynomial and a progressive plane shape is determined based on the polynomial. Further, in Patent Document 2, a target power is set everywhere in the lens, and the shape of the lens surface is determined based on the power.
However, all of these are calculated on the assumption that the optical performance data exists even if the optical performance data is somewhat inaccurate, and there is a guarantee that the lens surface shape is objectively suitable for the progressive power lens. There isn't.
Therefore, regarding a method of estimating a region in which optical performance data does not exist by interpolation calculation, a method capable of giving an appropriate optical performance aspect to the region even if optical performance data does not exist has been required.

First, the first means is an interpolation method for interpolating the optical performance of a region of unknown optical performance in a progressive refractive force lens (hereinafter referred to as an interpolation target lens) having a region of unknown optical performance. Therefore, for a plurality of progressive refractive power lenses, the distribution function of the optical performance is estimated based on the optical performance data in the region where the optical performance is unknown and the optical performance in the region where the optical performance is known adjacent or close to each other, and the distribution function of the optical performance is estimated. By applying the position information of the region where the optical performance is unknown to the distribution function, the optical performance of the region where the optical performance is unknown is calculated.
As a result, it is possible to acquire optical performance data in a region where the optical performance of the lens to be interpolated is unknown, which is close to the optical performance in that region when the optical performance is known.

"Optical performance" refers to the performance of the lens used in the evaluation of existing lenses, for example, S power, C power, equivalent spherical power (S + C / 2), astigmatism power and its axial power, prism amount and its Base value, prism direction, addition degree in progressive power lens, astigmatism, distortion, power error, etc. Further, the "optical performance data" is the unique numerical data of the lens capable of exerting those optical performances.
The "optical performance distribution function" is a function that expresses the optical performance of the lens surface defined by a set of a plurality of position data and optical performance data. The distribution function has the function of determining the output data based on the input data. In order to estimate the shape of the distribution function, it is better to assume an appropriate function model and estimate the parameters of the model by the least squares method or the like. Further, in order to estimate the lens surface with a smooth shape, the distribution function may be expressed by a quadratic form or a cubic form.
“Adjacent or close” means “adjacent” when a region whose optical performance is unknown and a region whose optical performance is known are in contact with each other at a boundary line, and “proximity” when they are not necessarily in contact with each other. As a specific pattern, for example, the center of the lens is the region where the optical performance is known and the outside is the region where the optical performance is unknown, or conversely, the outside is the region where the optical performance is known and the lens center. This is the case when the side is an unknown area. Alternatively, there is a case where a part of the lens is hollow and the optical performance is unknown. For example, even if a part of the lens is missing, the missing part is an area where the optical performance is unknown. The "region where the optical performance of the lens to be interpolated is unknown" and the "region where the optical performance of the plurality of progressive power lenses is unknown" are corresponding regions on the lens surface. The distribution function can be estimated by either "supervised learning" or "unsupervised learning", but supervised learning is easier and more accurate.
By applying "position information of a region where the optical performance is unknown" to the distribution function, it is possible to obtain optical performance data at an arbitrary position.

In the second means, when estimating the distribution function, when the optical performance data of a region whose optical performance is known is input, the optics of another region whose optical performance is known to be adjacent to or close to that region is known. Supervised learning is performed so that a value close to the performance is output.
By estimating in this way, it is possible to accurately obtain a distribution function that can be applied to a region where the optical performance of the lens to be interpolated is unknown. In particular, the output data can be data that creates a more appropriate distribution function by using the data in the region where the optical performance of the adjacent or adjacent regions is known as the teacher data.
Further, in the third means, supervised learning of the distribution function is performed using the positions of a plurality of points included in the region where the optical performance is known and the combination of the optical performance of the positions as input data.
That is, it is preferable to perform learning by using the combination of the positions of a plurality of points and the optical performance of the positions as specific teacher data. This increases the accuracy of estimating the distribution function in the region where the optical performance is unknown.
Further, in the fourth means, the positions of the plurality of points are arranged at equal angular intervals in the circumferential direction.
When estimating the distribution function from the center side of the lens to the outside, the distance in the circumferential direction becomes wider toward the outside. For example, points on the same circumference on two straight lines extending from the center of the lens are separated from each other toward the outside. When defining the correspondence of the position data of the area where the optical performance is unknown on the outside based on the position information of the area where the optical performance near the center of the lens is known, it is necessary to define the position data by the angle instead of the distance. This is because it becomes easier to set the correspondence.
Further, in the fifth means, the positions of the plurality of points are arranged at equal ratio intervals in the radial direction.
When estimating the distribution function from the center of the lens toward the periphery, the distance in the radial direction becomes wider toward the outside. For example, when comparing the fan-shaped region near the center of the lens with the outer fan-shaped region having a similar shape, the distance between the two points arranged in the radial direction is wider in the outer fan-shaped region. Therefore, by arranging the positions of the plurality of points arranged in the radial direction at geometric progressions, it is possible to correspond to the characteristics of the lens in which the spacing is geometrically large from the center of the lens. Further, by making the radial direction proportional to each other in this way, the distance between the data points is roughly set on the outside and finely set in the inner region. It is important that the progressive surface shape is smooth in the outer region, and it is desired that the value of the optical performance data changes smoothly. Therefore, it is advantageous to roughly arrange the arrangement in the outer region in this way. Further, the interval between the data points may be made finer in the inner region with respect to the outer region. In the vicinity of the center of the progressive power lens, the progressive power straight lens needs to control the power change and suppress the astigmatism in the central part of the progressive band, which complicates the optical performance distribution. This is because it is advantageous to do so.

Further, in the sixth means, the input data of the distribution function estimated by performing supervised learning is the optical performance data at discrete positions in the region where the optical performance is known.
By using the optical performance data at discrete positions during estimation, the distribution function can be estimated accurately without extremely increasing the number of input data.
Further, in the seventh means, the value estimated by supervised learning is set to be a parameter constituting a continuous function in a region where the optical performance is unknown.
By obtaining such a parameter of the distribution function, it becomes possible to easily calculate the shape in the region where the optical performance is unknown.
In the eighth means, the supervised learning is a set of the positions of a plurality of points included in the region where the optical performance is known, the combination of the optical performance of the positions, and the value of one coefficient to be calculated. Is used as one teacher data, and is performed based on a plurality of the teacher data.
This is because it is suitable for estimating the distribution function of the region where the optical performance is unknown, which requires collecting such teacher data. The more teacher data, the better.

Further, in the ninth means, the region where the optical performance is unknown is outside the region where the optical performance is known and is adjacent to or close to the region away from the center of the lens.
In particular, there are many regions where the optical performance is unknown in the outer region near the lens center region and away from the lens center. Therefore, the region for estimating the distribution function should be such a region.
Further, in the tenth means, when the lens to be interpolated is a minus intensity lens, the region where the optical performance is unknown is set to be a distance region.
The distance area is an area arranged above the lens for the wearer to see in the distance. This is because, in a negative intensity lens, the luminous flux is refracted in the direction of divergence, so that a region whose optical performance is unknown is likely to occur in the distance region due to its characteristics.
Further, in the eleventh means, when the lens to be interpolated is a positive intensity lens, the region where the optical performance is unknown is set to be a near-use region.
The near area is an area arranged below the lens for the wearer to see near. This is because in a plus-intensity lens, the luminous flux is refracted in the direction of concentration, and due to its characteristics, the luminous flux is concentrated in the near-field region, so that an region whose optical performance is unknown is likely to occur.
The scope of the invention is not limited to the configurations expressly described herein, but also includes combinations of various aspects of the invention disclosed herein. Of the present invention, the configuration for which a patent is sought is specified in the appended claims, but even if the configuration is not currently specified in the claims, it is disclosed in the present specification. We intend to make this configuration the scope of claims in the future.
The invention of the present application is not limited to the configuration described in the following embodiments. The components of each embodiment and modification may be arbitrarily selected and combined. Further, any component of each embodiment or modification, and any component described in the means for solving the invention or a component described in the means for solving the invention are embodied. And may be configured in any combination. We also intend to acquire the rights to these in the amendment or divisional application of the present application.

In the present invention, it is possible to acquire optical performance data in a region where the optical performance of the lens to be interpolated is unknown, which is close to the optical performance of the region when the optical performance is known.

The block diagram explaining the machine learning apparatus which realizes the interpolation method of this invention. Flow chart of the first routine for creating teacher data and estimating the coefficient of the distribution function of the optical performance in the region where the optical performance is unknown. The flowchart of the second routine which estimates the optical performance of the region where the optical performance of the lens to be interpolated is unknown by using the learning result. Explanatory drawing explaining the reference point included in the inner fan-shaped area and the point outside the reference point. Explanatory drawing explaining the setting method of the reference point included in the inner fan-shaped area. The average power distribution diagram and the astigmatism distribution diagram of the progressive power lens of Example 1, the upper row is the state before interpolation, the middle row is the result of interpolation in the present embodiment, and the lower row is the result of interpolation by the conventional method. The average power distribution diagram and the astigmatism distribution diagram of the progressive power lens of Example 2, the upper part is the result of calculating up to φ80 by simulation, and the middle part is the result of interpolating φ50-80 in this embodiment. The lower row is the result of interpolating φ50 to 100 in this embodiment. The average power distribution diagram and the astigmatism distribution diagram of the progressive power lens of Example 3, the upper row is the state before interpolation, the middle row is the state after interpolation in the present embodiment, and the lower row is the interpolation by the conventional method. The result. In Example 5, (a) is an explanatory diagram for explaining the interpolation of the defective portion when the progressive power lens has a strong negative power, and (b) is the interpolation of the defective part when the progressive power lens has a strong positive power. Explanatory drawing explaining. An explanatory diagram of an average frequency distribution for explaining interpolation of a hidden mark portion as a data missing portion in the sixth embodiment.

Hereinafter, embodiments of an interpolation method for interpolating the optical performance of an unknown region of the progressive power lens of the present invention will be described.
First, an example of a schematic configuration of a peripheral device that executes an algorithm for interpolating the optical performance of an unknown region of a progressive power lens will be described.
FIG. 1 is a schematic block diagram of the machine learning device 1 according to the embodiment. The machine learning device 1 is composed of, for example, a general-purpose computer device. The machine learning device 1 is composed of a CPU (central processing unit) (not shown) and peripheral devices such as a storage device 2 composed of a ROM, RAM, and the like. The storage device 2 can be composed of a hard disk device (HDD) or a solid state drive (SSD). The storage device 2 stores position data and optical performance data of a plurality of progressive power lenses serving as monitor lenses. The CPU executes various arithmetic processes by calling and executing various programs stored in the storage device 2. An input means 3 (for example, a keyboard, a mouse, etc.) and an output means 4 (for example, a monitor, a printer, etc.) are connected to the machine learning device 1.

The machine learning device 1 has a function of learning an algorithm for estimating the distribution function of the optical performance in a region where the optical performance is unknown based on the optical performance data in the region where the optical performance is known for a plurality of progressive power lenses.
The machine learning device 1 includes a teacher data creation unit 5 for executing an algorithm, a distribution function calculation unit 6, and an interpolation calculation unit 7. The teacher data creation unit 5 creates teacher data by executing a machine learning program stored in the storage device 2. Further, the teacher data creation unit 5 is a data calculation unit that converts arbitrary data of the progressive refraction lens into standardized data of JCC (Jackson Cross Cylinder), and estimates a distribution function from arbitrary data of a plurality of progressive refraction lenses. It has a data acquisition unit for creating teacher data for.
The distribution function calculation unit 6 performs supervised learning based on the data created by the teacher data creation unit 5, and stores the estimated distribution function in the storage device 2. The interpolation calculation unit 7 calls the distribution function from the storage device 2 and applies the position data and the optical performance data of the progressive power lens (hereinafter, the lens to be interpolated) having a region whose optical performance is unknown to the optical performance of the lens to be interpolated. Has a function of estimating the optical performance in an unknown region.
The function for estimating the optical performance in the region where the optical performance of the lens to be interpolated is unknown may be separated from the machine learning device 1 and realized by another device.

Next, the routine of the algorithm executed by the CPU of the machine learning device 1 will be described with reference to the flowcharts of FIGS. 2 and 3.
First, a first routine for creating teacher data based on FIG. 2 and estimating the coefficient of the distribution function of the optical performance in a region where the optical performance is unknown will be described.
In step S1, based on the input, optical performance data corresponding to the positions of a plurality of progressive power lenses to be monitor lenses are acquired. A "monitor lens" is a reference lens from which optical characteristic data for creating learning data can be acquired. The optical performance data used here are three data of the average dioptric power component mdp, the horizontal and vertical astigmatism component J00, and the oblique astigmatism component J45 standardized by JCC. JCC is expressed by the following equation (1).

The J00 component of surface astigmatism is the difference between the horizontal refractive power and the vertical refractive power. In order to judge this, it is preferable to partially differentiate the shape of the refracting surface. More specifically, the sag value of the surface shape expressed by the function of x and y is partially differentiated. Then, the J00 component of surface astigmatism is proportional to the difference between the value of the derivative that is partially differentiated with respect to x and the value of the derivative that is partially differentiated with respect to y. Here, an example of a method of calculating the value of the derivative obtained with the second partial derivative with respect to x is shown.
In finding the value of the derivative that has been differentiated by one degree in the x direction at a certain coordinate (x, y), (x + Δ, y) and (x−Δ, y) are used as the functions representing the sag value of the surface shape. Substitute each and divide the difference between the obtained function values by 2Δ. Then, in finding the value of the derivative that was differentiated by two deviations in the x direction at a certain coordinate (x, y), it was differentiated by one deviation in the x direction at (x + Δ, y) and (x−Δ, y). The values of the derivatives may be obtained and the difference may be divided by 2Δ. The y direction is calculated in the same manner. Here, Δ is an appropriate minute amount, for example, 0.1 mm.
The J45 component of surface astigmatism is the difference between the refractive power in the 45-degree diagonal direction and the refractive power in the 135-degree diagonal direction. It expresses the sag value of the surface shape as a function of x and y, and is proportional to the difference in the value of the derivative obtained by partially differentiating the surface shape in the 45-degree diagonal direction and the 135-degree diagonal direction, respectively. The following is an example of a method for calculating the value of the derivative that is partially differentiated in the diagonal direction.
In finding the value of the derivative that has been differentiated by one degree in the diagonal 45 degree direction at a certain coordinate (x, y), the functions representing the sag value of the surface shape are (x + Δ, y + Δ) and (x−Δ). , Y−Δ) may be substituted respectively, and the difference between the obtained function values may be divided by 2√2Δ. Then, in finding the value of the derivative that is differentiated by two deviations in the diagonal 45 degree direction at a certain coordinate (x, y), it is one deviation at (x + Δ, y + Δ) and (x−Δ, y−Δ). The values of the derivative obtained by the derivative of the order may be obtained, and the difference may be divided by 2√2Δ. The diagonal 135 degree direction is calculated in the same manner.
The optical performance data may be obtained as a result of a simulation based on the shape data, or the result obtained by measuring with a measuring device such as a mapping device may be converted into JCC data. The optical performance data may be created by the simulation software of the machine learning device 1, or may be imported from a database created by another general-purpose computer device linked with the machine learning device 1.

In step S2, teacher data is created based on the optical performance data of the monitor lens acquired in step S1. The method of acquiring teacher data will be described later.
In step S3, learning is performed based on the teacher data created in step S1, and the coefficient of the distribution function of the optical performance in the region where the optical performance is unknown is estimated.
This ends the first routine once, and the second routine for estimating the optical performance in the region where the optical performance of the lens to be interpolated is unknown is executed based on the input using this learning result. This will be described with reference to FIG.
When a region in which the optical performance of the lens to be interpolated is unknown is set in step S11, the distribution function is estimated in step S12 based on the known optical performance data of the region adjacent to the region. In step S13, the optical performance data of typical points in the region where the optical performance is unknown is estimated, interpolation calculation is performed based on those points, and the optical performance data of the lens to be interpolated is combined.

Next, an example of a method for creating teacher data executed in the above routine and a specific method for obtaining a distribution function based on the teacher data will be described.
1. 1. Concept of Learning The present invention estimates the distribution function of the optical performance in the region where the optical performance of the lens to be interpolated is unknown based on the known optical performance data of a plurality of progressive refractive power lenses to be monitor lenses, and the lens to be interpolated. The position information of the region where the optical performance is unknown is applied to the distribution function to estimate the optical performance of the region where the optical performance is unknown.
Specifically, it is assumed that the progressive power lens to be the interpolation target lens is in a situation where optical performance can be obtained at an arbitrary position in the φ60 region, for example. This is, for example
B) As the optical performance distribution that is the target of the design, the values of each component of JCC are set discretely at the grid points at intervals of about 2 mm to 4 mm. B) By mapping measurement with a lens manufactured by another company A set of S power, C power, and astigmatic axis is measured at lattice points at intervals of about 1 mm to 2 mm, and it is assumed that each set of measured values is converted into JCC. It is assumed that the value between points can be calculated by spline interpolation. In this situation, the optical performance outside φ60 is estimated to be about φ80 to φ100.
As an example, the monitor lens creates teacher data using 50 types of progressive power lenses, and estimates the optical performance outside the area that is the "data area that is the basis of estimation" based on the created teacher data. To do.
This method is an example, and another method can be considered.

First, here, as shown in FIG. 4, the fan-shaped shape is based on 25 points (hereinafter, these points are used as reference points) included in the inner fan-shaped region E1 on the monitor lens surface with φ40 as a boundary. Consider a method of estimating four points outside a, b, c, and d in the diametrical direction located in the center of the outer circumference of the region E1 (that is, the position of the apex of the sector). That is, these 25 reference points are "data that is the basis of estimation". The reference point does not have to be 25 points. The fan shape inside and outside has a similar shape and is suitable for estimating the distribution function, so it is illustrated, but the "data area from which the estimation is based" does not have to have a similar shape. Further, the 25-point fan-shaped regions E1 can be set adjacent to each other according to the outer fan-shaped regions to be acquired, such as φ40, φ50, and φ60. Further, although the fan shape is taken as an example for ease of explanation, the shape is not limited to the region where the optical performance is unknown and the region where the optical performance is known adjacent thereto.
As the reference points, five reference points were set at equal intervals in the radial direction in five directions at intervals of 15 degrees. Since it is set at intervals of 15 degrees in the circumferential direction, it is a sequence of points that radiate out in 24 directions.
In addition, the data in the radial direction of the reference point was considered in this way. For example, when the φ40 region is set, it is conceivable that the distance from the center is an even distance such as 20, 17, 14, 11, and 8 mm. However, in that method, when the region diameters of the reference points are different, the arrangements in the angular direction and the radial direction are not similar. Therefore, in the embodiment, it is preferable to arrange the reference points in the radial direction at equal ratio intervals of 2 to the 1/4 power = 1.189207 ....

Even when the optical performance of the four points outside a, b, c, and d shown in FIG. 4 is estimated based on the above reference points, the position information of the region where the optical performance of the lens to be interpolated is unknown can be obtained. However, the optical performance of the four points cannot be obtained so smoothly. This is because each point is estimated separately and connected.
Therefore, this idea is extended so that the distribution of the outer optical performance is expressed in the quadratic form or the cubic form instead of the values of the optical performance of the outer four points. To explain concretely based on FIG. 4, first, from the JCC value of the 5 reference points B on the outermost side of the inner fan shape and the JCC value of 20 points on the outer side, the fan Subtract the JCC value of the reference point B of the apex (point X coordinate 0 and Y coordinate 20 in FIG. 4) (as a result, mdp, J00, and J45 are all 0 at the reference point B of the apex of the fan). Learning is performed to find a distribution function that represents this "value of the subtracted result". By substituting the coordinates (position data) into the distribution function and adding the JCC value of the apex of the fan to the result obtained, the optical characteristics of the region where the optical performance is unknown can be obtained.
The fan-shaped apex is set as the origin position, the radial and circumferential values at that position are set to 0, and the apex data is used as a constant component of the interpolation formula. By doing this, the interpolation expression is always smoothly connected to the vertices.
Since one interpolation formula can be obtained in one fan-shaped region E1, it is preferable to make 24 interpolation formulas by changing the angle of the fan in order to estimate the optical performance of the entire circumference. When interpolating a plurality of outer fan-shaped regions E2 in this way, the outer fan-shaped regions E2 to be interpolated are adjacent to each other. In that case, it is necessary to interpolate the optical performance data of the adjacent outer fan-shaped regions E2 in order to smoothly connect the interpolation formulas of the adjacent outer fan-shaped regions E2. For this reason, for example, a smooth distribution can be obtained by weighted averaging the values obtained by five adjacent interpolation formulas.
For example, the position d in FIG. 4 is the X coordinate 0Y coordinate 40. Consider a method of obtaining the JCC at the position d by "weighted average of the values obtained by five adjacent distribution functions". It is natural that the weight of the result of using E1 and E2 in FIG. 4 as they are is the heaviest, and the weight is set to 4, for example. The sectors E1 and E2 are shifted by one column clockwise and counterclockwise, respectively, and another distribution function is created, and the weight of the obtained value is 2. Further, the weight of the value obtained by creating another distribution function by shifting the distribution function clockwise and counterclockwise by two columns is set to 1.
Here, the weights are represented by integers 1, 2, 4, 2, 1, but these values are multiplied by one of the JCC3 elements at the position d calculated by each distribution function and added together. The weighted average can be obtained by dividing the result by 10.
Here, the weighted average of 1: 2: 4: 2: 1 is applied to the outermost part of the sector E2. Further, the innermost side of the fan type E2 is set to 0: 0: 10: 0: 0. That is, the weight of the polynomial based on the front and back fan shapes is set to 0. Then, the weight of the weighted average is smoothly changed from 0: 0: 10: 0: 0 to 1: 2: 4: 2: 1 from the inside to the outside of the fan-shaped E2. As described above, the calculation procedure for changing the weighted average weight as the distance from the fan type E2 increases is somewhat complicated. However, for example, at a position immediately outside the reference point B of the apex of the fan (a position closer to B than the point a), it is natural that the value of JCC at the reference point B of the apex of the fan is closest. In other words, the influence from the position before and after the reference point B at the apex of the fan in the circumferential direction is smaller than the influence from the point B. Then, at a position away from the fan-shaped E2 (as the distance from b, c, and d in the figure increases), the influence from the fan-shaped region having the reference point B, the point B + 1, and the point B-1 of the apex of the fan as the apex The learning results can be used while reflecting that the difference is getting smaller.

2. Creation of teacher data An example of an equation that interpolates based on the reference point of the monitor lens group, that is, a method of creating teacher data for estimating the distribution function will be described.
1) Definition of the outer fan-shaped area Set polar coordinates (r, s) with the radial direction as the r coordinate and the circumferential direction as the s coordinate. However, the outside is positive in the radial direction, and the counterclockwise direction is positive in the circumferential direction. The unit of r and s is the interval between reference points. With the coordinates of the fan apex in the inner region as (0, 0), the amount by which each component of JCC in the outer fan-shaped region E2 increases or decreases with respect to the apex position of the fan is represented by a polynomial up to the third order of r and s. By not providing a constant term in this polynomial, a smooth connection from the inner sector region E1 to the outer sector region E2 at the apex position of the fan is guaranteed.
Then, by weighted averaging with a plurality of sectors, all the boundaries are smoothly connected. An example of a specific weighted average will be described below.
f _mdp (r, s) = A ₀ r ³ + A ₁ r ² s + A ₂ rs ² + A ₃ s ³ + A ₄ r ² +
A ₅ rs + A ₆ s ² + A ₇ r + A ₈ s
Since this is an interpolation formula for the average frequency mdp and is also a distribution function of J00 and J45, it is _{necessary to make f J00} (r, s) and f _J45 (r, s) in the same manner.
In order to obtain the optical performance of the outer fan-shaped region E2, the respective coefficients _{of A 0 to} A _{8 of f mdp} (r, s), f _J00 (r, s) and f _J45 (r, s) are obtained. There is a need. That is, it is necessary to determine 9 × 3 = 27 values.

_{Now, f mdp (r,} s) the _{A 0} by way of example how to obtain training data for the outer region will be described.
To determine the A ₀ is a one certain value, the argument is used 75 a function. Let it be g _mdp0 . The 75 arguments are the optical performance data of the 25 points of the JCC3 element in the inner fan-shaped region E1. That is, here, in order to obtain the coefficient of the distribution function of the outer fan-shaped region E2, the data of the inner fan-shaped region E1 is used.
The function can be expressed, for example, as follows.
g _mdp0 (mdp ₀₁ , mdp ₀₂ … mdp ₂₅ , J00 ₀₁ , J00 ₀₂ … J00 ₂₅ , J45 ₀₁ , J45 ₀₂ … J45 ₂₅ )

A total of 27 types (27) of such functions are determined according to the coefficients of _{A 0 to} A ₈ , such as g _mdp0 … g _mdp8 , g _J000 … g _J008 , g _J450 … g _J458. To do.
_{In this embodiment, a function such as gmdp0} defined in this way is expressed as a third-order polynomial with 75 arguments. This expression is an example.
The polynomial representing one function g _mdp consists of 451 terms in total. The constant term consists of one constant, and the other terms are coefficients multiplied by one or more arguments. Therefore, it is one constant and 450 coefficients that make up the polynomial. The polynomial is divided into terms and shown as follows. Although the terms mdp, J00, and J45 were not used as cubic terms for the sake of program simplification, they may be used.
Factor ... 25 × 3 kinds of constants ... one primary term of constant term (mdp, J00, J45) = 75 pieces 2 order coefficient ... 25 × 3 kinds of ^(mdp 2, ^J00 2, J45 ²⁾
+25 pcs x 3 types (mdp / J00, mdp / J45, J00 / J45) = 150 pcs Coefficient of cubic term ... 25 pcs x 3 types (mdp ³ , J00 ³ , J45 ³ )
+25 pieces × 6 types ^{(mdp 2 · J00, mdp ·} J00 2,
^{mdp 2 · J45, mdp · J45} 2,
J00 ² / J45, J00 / J45 ² ) = 225 pieces

One teacher data consists of a set of 25 × 3 = 75 arguments and _{one value that a function (eg, gmdp0} ) should take. For example, in one monitor lens, 25 fan-shaped regions have 24 patterns in the circumferential direction. If the fan-shaped region is shifted in the radial direction and there are 4 patterns, then 24 × 4 = 96 patterns. Since there are 50 types of monitor lenses, 4800 teacher data can be obtained. Using these teacher data, machine learning of 451 constants and coefficients based on the teacher data under the condition that the error from the value that the function should take is minimized (the sum of squares of the error is minimized). To decide with. In the embodiment, the least squares method is used.
When this machine learning is _{executed for a total of 27 pieces of g mdp0} … g _mdp8 , g _J000 … g _J008 , g _J450 … g _J458 , the preparation for interpolating the optical performance is completed. This is a calculation for obtaining 451 × 27 = 12177 numerical values.

3. 3. Calculation of coefficient of distribution function-estimation of optical characteristics of outer fan-shaped region 27 values (75 in total) of JCC3 elements at predetermined 25 points inside one inner sector, including _gmdp0 By substituting into the function of, 27 coefficients can be obtained. Nine of them correspond to fmdp (r, s), another nine correspond to fJ00 (r, s), and the remaining nine correspond to the coefficients _{A 0 to} A _{8 of fJ45 (r, s). As a result, three functions f mdp} (r, s), f _J00 (r, s) and f _J45 (r, s), which are distribution functions corresponding to the fan shape, are determined.
Since the coefficients of the three functions (distribution functions) have been obtained, the values of the JCC3 elements can be obtained by substituting the values of the variables r and s that represent arbitrary positions of the outer sector area E2 adjacent to the inner sector area E1. be able to. The contents of machine learning for calculating the outer fan-shaped region E2 will be described in more detail.
First, the main 25 points of the inner fan-shaped region E1 are defined. As shown in FIG. 5, a line segment is drawn from the point P toward the center O of the lens, the length thereof is R, and the point where the line segment intersects the circle of φ60 is the fan vertex Q. Two points are set in a counterclockwise 15-degree step from point Q, and two points are set in a clockwise 15-degree step. Then, 5 points are set on the circumference of φ60 in the circumferential direction including the point Q. Let the points be Q + 2, Q + 1, Q, Q-1, and Q-2.
The optical performance of the lens to be interpolated can be calculated everywhere in the φ60 region. Alternatively, at least, the optical performance is known with respect to points such as Q, Q1, Q2, Q3, Q4, Q + 2, Q + 1, Q-1, and Q-2. In that situation, we would like to estimate the optical performance distribution outside the φ60 region.
Next, the position of the point sequence on the line from the point Q to the lens center O is determined. 2 of the fourth root of a value (1.1892071 ...) expressed in T, and sets a point to _{Q 1} 30 / Tmm from the center, then set the 30 ^{/ T} 2 point _{Q 2} mm from the center O, further sets a point _{Q 3} of the center O from 30 ^{/ T} 3 mm, to set the point _{Q 4} from the center 30/2 = 15 mm at the end. Then, 5 points are set toward the center including the point Q. Similarly for 4 points other than the row of Q arranged on the circumference of φ60 circle, a total of 25 points are determined with the points Q + 2, Q + 1, Q-1, and Q-2 as the row of fan vertices.

The JCC at the determined 25 points is calculated, and based on the values, nine coefficients for each of fmdp (r, s), fJ00 (r, s), and fJ45 (r, s) are calculated. The coordinates of the point P with respect to the point Q are
r = log (R / 30) / log (T)
s = 0
Since it is given by, substitute r and s into fmdp (r, s), fJ00 (r, s), and fJ45 (r, s) to obtain the value of each function, and give them mdp, J00, at the point Q. By adding the values of J45, the values of mdp, J00, and J45 at the point P are obtained. This operation is performed at all the main points of the outer fan-shaped region E2 to obtain the values of mdp, J00, and J45, and the points between the points are interpolated by a known calculation method.
According to the above formula, for example
When the point P is at the position of the point Q, R = 30 and r = 0. When the point P is on the line connecting the center and the point Q, the s coordinate of the point P is always s = 0 even if the value of R changes variously.
・ When the point P is at a position of 42.426 mm from the center, R = 42.426.
r = log (42.426 / 30) / log (T)
= Log (2 ^1/2 ) / log (2 ^1/4 )
= 2.
When the point P is at the position of the point Q + 1, R = 30 and r = 0. When the point P is on the line connecting the center and the point Q + 1, the s coordinate of the point P is always s = 1 even if the value of R changes variously.
When the point P is at the position of the point Q-2, R = 30 and r = 0. When the point P is on the line connecting the center and the point Q-2, the s coordinate of the point P is always s = -2 even if the value of R changes variously.

In the embodiment of the above configuration, the following effects are obtained.
(1) An arbitrary region where the optical performance is unknown The distribution function of the optical performance is estimated based on the optical performance data of the adjacent region where the optical performance is known, and the position information of the region where the optical performance of the lens to be interpolated is unknown. Can be applied to the distribution function to accurately estimate the optical performance of an unknown region.
(2) There are 50 types of monitor lenses, but the obtained teacher data is 4800. You can get more by increasing the reference points. On the other hand, the number of monitor lenses can be further reduced. In this way, sufficient teacher data can be created even if the number of monitor lenses is not large, and the distribution function of the optical performance in the region where the optical performance is unknown can be estimated from the teacher data, so that the optics in the region where the academic performance is unknown can be estimated. It is an excellent method for estimating performance.
(3) When acquiring the teacher data, the position data in the radial direction is arranged at equal ratio intervals of 2 to the 1/4 power = 1.189207 .... Setting in this way can correspond to the characteristics of the lens in which the distance from the center of the lens increases in a geometric progression. Further, by making the radial direction proportional to each other in this way, the interval between the data points can be roughly made on the outside, which is advantageous for setting the value of the optical performance data to be smoothly changed. ..
(4) Since the arguments of r and s of the distribution function are defined in polar coordinates, it is easy to calculate the setting of the position data of the object having a circular shape called a lens.

(Example 1)
In the first embodiment, the peripheral φ50 to 80 region of the lens whose spherical shape is known is interpolated by the method of the embodiment. FIG. 6 is a distribution diagram of a progressive power lens interpolating a region where specific optical performance is unknown according to the embodiment of the above embodiment. The upper part is an average dioptric power distribution diagram and an astigmatism distribution diagram showing the average dioptric power and astigmatism of a φ50 round lens acquired. The middle row is an average power distribution diagram and an astigmatism distribution diagram in which the three elements of JCC outside the φ50 round lens interpolated by the method of the above embodiment are estimated. The lower part is an average power distribution diagram and an astigmatism distribution diagram as comparative examples in which the three elements of JCC outside the φ50 round lens are estimated by the conventional method.
The average frequency is the same as the mdp used in the above calculation. Astigmatism is obtained by doubling each of J00 and J45, adding the squares, and then taking the square root as in the equation of Equation 2.

As the above-mentioned conventional method, the extrapolation method is used here.
For example, suppose that the value of mdp is as follows.
Reference point B at the apex of the fan: x0 (Specific example 0.14D)
One below the reference point B at the apex of the fan: x1 (Specific example 0.11D)
Two below the reference point B at the apex of the fan: x2 (Specific example 0.10D)
If extrapolating with a linear equation based on these,
Point a: x0 + (x0-x1) = 2x0-x1
Point b: x0 + 2 (x0-x1) = 3x0-2x1
Point c: x0 + 3 (x0-x1) = 4x0-3x1.
Specific numerical value a point: 0.17D
Point b: 0.20D
point c: 0.23D
Thus, it is a method of determining the numerical value of the unknown region based on the point that the optical performance is already known. In some cases, a quadratic equation is used.
It can be seen that in the case of interpolation in the present embodiment, there is no large variation in the average dioptric power and the value of astigmatism outside φ50, and the interpolation is performed with reasonable optical performance of the lens. On the other hand, in the conventional example, the values of the average power and the astigmatism become large even outside the φ50, and it cannot be said that the shape is very appropriate for the design of a normal progressive power lens of this type.

(Example 2)
In the second embodiment, the peripheral φ50 to 100 region of the lens whose spherical shape is known is interpolated by the method of the embodiment. FIG. 7 is a distribution diagram of a progressive power lens interpolating a region where specific optical performance is unknown according to the embodiment of the above embodiment. The upper part is an average dioptric power distribution diagram and an astigmatism distribution diagram showing the average dioptric power and astigmatism obtained by simulating a round lens of φ80. The middle stage is an average power distribution diagram and an astigmatism distribution diagram in which the three elements of JCC up to φ80 on the outside of the φ50 round lens interpolated by the method of the above embodiment are estimated. The middle row is an average power distribution diagram and an astigmatism distribution diagram in which the three elements of JCC up to φ100 on the outside of the φ50 round lens interpolated by the method of the above embodiment are estimated.
Comparing the simulation results with the estimation results of the method of the above embodiment for the upper and middle φ80 round lenses, the estimation by the method of the above embodiment shows the optical performance in line with the results of the simulation from the relatively shape. You can see that. Therefore, it is inferred that a round lens of φ100 would be close to the simulation result if the lens was up to φ100.

(Example 3)
In the third embodiment, the peripheral φ70 region of the lens whose spherical shape is known is interpolated by the method of the embodiment. FIG. 8 is a distribution diagram of a progressive power lens interpolating a region where specific optical performance is unknown according to the embodiment of the above embodiment. The upper part is an average frequency distribution diagram and an astigmatism distribution diagram showing the average frequency and astigmatism of the spherical shape acquired. The middle row is the average frequency distribution map and the astigmatism distribution map interpolated by the method of the above embodiment. The lower part is the average frequency distribution map and the astigmatism distribution map in which the three elements of the JCC outside the spherical shape are estimated by the conventional method. The conventional method is an extrapolation method as in Examples 1 and 2 above.
It can be seen that there is no significant change in the outer curve of the lens shape when interpolated in the present embodiment, and the interpolation is performed with reasonable optical performance of the lens.

(Example 4)
Example 4 is the reverse pattern of Example 1. When the optical performance of the outer fan-shaped region E2 is known, the optical performance data of the inner fan-shaped region E1 can be estimated from the outer fan-shaped region E2 as in the learning method of the embodiment. That is, as in the embodiment, however, teacher data having the opposite pattern is created and learned, and the values of mdp, J00, and J45 of the inner fan-shaped region E1 are obtained based on the 25 points of the fan-shaped region E2. To do. The teacher data already created in Example 1 may be used. This may be to obtain the values of the main 25 points. First, the distribution function of the inner fan-shaped region E1 is estimated, and the outer fan-shaped region E2 is applied to the distribution function to apply the outer fan-shaped region E2 to the inner fan-shaped region E1. The values of mdp, J00, and J45 may be obtained.

(Example 5)
The fifth embodiment is a case of estimating a region where the optical performance is unknown, which occurs when the progressive power lens is a lens having a strong negative power or a strong positive power.
For a progressive power lens with a negative power, if the distance power is in the range of S-4.0 to +3.00D and the addition power is ADD1.00 to 3.00D, performance data in the φ50 region can be measured without problems with many devices. it can.
However, in the case of a strong negative power such as the distance power S-8.00D, the measurement data of the optical performance in the region far from the center is likely to be lost. This is because when the light beam incident on the lens is emitted, it spreads out of the lens region and does not reach the light receiving portion. In this case, it is not possible to obtain information about the lens performance at the position where the light beam that did not reach the light receiving portion was transmitted. This tendency is remarkable in the region above the lens. Such a defect is likely to occur in the shaded portion of FIG. 9A. Therefore, the distribution function of the optical performance can be estimated based on the inner region or the lateral region where the optical performance is known adjacent to the defect portion.
On the other hand, in a progressive power lens having a positive power, when the positive power for distance use is strong and the addition power is also strong, the measurement data of the optical performance is likely to be lost, especially in the lower region of the lens. This is because the positions where the light rays reach the CCD are concentrated, so that the performance at each position of the lens cannot be calculated correctly. Such a defect is likely to occur in the shaded portion of FIG. 9B. Therefore, the distribution function of the optical performance can be estimated based on the inner region or the lateral region where the optical performance is known adjacent to the defect portion.

(Example 6)
Example 6 is an example of compensating for the lack of measurement data in the vicinity of the hidden mark of the lens. The hidden mark is a ○ -shaped mark that is attached to the lens so that the user cannot see it. The hidden mark is usually formed around a position 17 mm away from the geometric center of the progressive lens on the ear side and the nasal side. However, characters may be engraved at a position several millimeters above and below it. At the optician shop, the hidden mark is used to determine the position to put the frame. In many cases, the eye point is located between the two hidden marks or above and below the hidden mark by a predetermined distance. The letters are information about lens products. This is because if you have this letter, you can tell which product was made by which manufacturer based on the lens in the frame. Since there is a hidden mark, the optical performance in the area of the hidden mark cannot be measured. Therefore, it is necessary to estimate the optical performance of the hidden mark.
For example, when estimating the area of the hidden mark S on the ear side,
a. Interpolate from the inside to the outside.
b. Interpolate from the outside to the inside.
c. Interpolate clockwise and counterclockwise in the direction of rotation.
As described above, the four average values are adopted. However, in reality, as shown in FIG. 10, b. Since it is often the case that optical performance data in the above region cannot be obtained, in that case, an average value of three is adopted. If the area to be interpolated is large (wide), it is conceivable to use a weighted average. Specifically, the weight is small for the result of interpolation in which the area where the data to be the basis of other calculation is located is far, and the weight is large in the result of interpolation in which the area is close.

The above-described embodiment is merely described as a specific embodiment for exemplifying the principle of the present invention and the concept thereof. That is, the present invention is not limited to the above-described embodiment. The present invention can also be embodied in a modified manner as follows, for example.
-In the above embodiment, there are three types of data, mdp, J00, and J45, but a prism component may be further included. This idea is effective in the calculation of estimating astigmatism for lenses with strong negative and positive degrees.
-In the above, the fan shape includes five points at intervals of 15 degrees in the circumferential direction, but the present invention is not limited to this. For example, it can be freely changed to 36 points at 10 degree intervals or 48 points at 7.5 degree intervals. Rather than having a fan shape that is long in the circumferential direction or long in the radial direction, stable interpolation calculation can be performed if the point spacing is about the same in both directions.
-In the above embodiment, data is obtained at the positions of 25 main points as the inner region, but the data is not limited to 25 points. You may try to get a very large number to make a more accurate estimate. Further, when the number is too large, the dimension may be reduced by the principal component analysis, and the correspondence may be created based on the top 10 principal component data.
-Although it is conceivable to use deep learning for the estimation calculation, a quadratic form of least squares estimation that does not consider the interaction may be used.

-Mdp, J00, and J45 may be added as cubic terms in 27 kinds of function expressions of g _mdp0 ... g _mdp8 , g _J000 ... g _J008 , and g _J450 ... g _J458.
-The calculation with point Q + 1 as the fan apex and s = -1 with the point Q-1 as the fan apex is performed separately, and the average value or the weighted average (with the weight of Q increased) is performed separately. You may adopt the value. Further, the result of setting s = -2 with the point Q + 2 as the fan apex and the result of setting s = 2 with the point Q-2 as the fan apex may be considered. By doing so, the optical performance in the outer region can be obtained as a more stable numerical value.
-When estimating the optical characteristics of the outer fan-shaped region E2, a large calculation cost is required to execute the estimation for all points in the outer region. Therefore, a method may be used in which the JCC at the position of a representative point in the outer region is obtained in advance and the interpolation calculation is performed based on those values. Typical points may be in a grid pattern. Alternatively, the circumferential direction may be 24 points at intervals of 15 degrees, and the radial direction may be 30T mm, 30T ^{2 mm, 30T 3} mm, or 60 mm from the center.
-The coefficient group used for the interpolation calculation in the above-mentioned Example 6 is referred to as c. It may be shared clockwise and counterclockwise. The merits of sharing are that the learning data used for each interpolation calculation is doubled, and that the interpolation calculation is balanced without making a big difference between the nasal side and the ear side of the lens. Furthermore, a. And b. It is also possible to share it with. However, the difference in the properties of the outward interpolation and the inward interpolation is considered to be larger than the difference between clockwise and counterclockwise, so it is not always good.
-In the above, the case where the region where the optical performance is unknown and the region where the optical performance is known are "adjacent" is given as an example. However, the two regions are not necessarily in contact and may be based on "close" regions.

Claims (11)

This is an interpolation method for interpolating the optical performance of a region of unknown optical performance in a progressive power lens (hereinafter referred to as an interpolation target lens) having a region of unknown optical performance.
For a plurality of progressive refractive power lenses, the distribution function of the optical performance is estimated based on the optical performance data of the region where the optical performance is known adjacent to or close to the region where the optical performance is unknown, and the lens to be interpolated. By applying the position information of the region where the optical performance of the lens is unknown to the distribution function, the optical performance of the region where the optical performance is unknown is calculated. Interpolation method for interpolating. When estimating the distribution function, when the optical performance data of a region where the optical performance is known is input, a value close to the optical performance of another region where the optical performance is known is output, which is adjacent to or close to that region. The interpolation method for interpolating the optical performance of an unknown region of a progressive power lens according to claim 1, wherein supervised learning is performed. Supervised learning is performed to estimate the configuration of the distribution function according to the input data, using the positions of a plurality of points included in the region where the optical performance is known and the combination of the optical performance of the positions as input data. The interpolation method for interpolating the optical performance of an unknown region of the progressive power lens according to claim 2. The interpolation method for interpolating the optical performance of an unknown region of a progressive power lens according to claim 3, wherein the positions of the plurality of points are arranged at equal angular intervals in the circumferential direction. The interpolation method for interpolating the optical performance of an unknown region of a progressive power lens according to claim 3 or 4, wherein the positions of the plurality of points are arranged at equal ratio intervals in the radial direction. Any of claims 2 to 5, wherein the input data of the distribution function estimated by performing supervised learning is optical performance data at discrete positions in a region where the optical performance is known. An interpolation method for interpolating the optical performance of an unknown region of the described progressive power lens. The progressive power according to any one of claims 2 to 6, wherein the value estimated by supervised learning is a parameter constituting a continuous function in a region where the optical performance is unknown. An interpolation method for interpolating the optical performance of an unknown region of a lens. In the supervised learning, the positions of a plurality of points included in the region where the optical performance is known, the combination of the optical performance of the positions, and the set of the values of one coefficient to be calculated are used as one supervised data. The interpolation method for interpolating the optical performance of an unknown region of a progressive power lens according to claim 2 to 7, which is performed based on a plurality of the supervised learning data. The progressive refraction according to any one of claims 1 to 8, wherein the region whose optical performance is unknown is outside the region where the optical performance is known and is located in a region adjacent to or close to the side away from the center of the lens. An interpolation method for interpolating the optical performance of an unknown region of a power lens. When the lens to be interpolated is a negative intensity lens, the region where the optical performance is unknown is a distance region, and the optical performance of the progressive power lens in the unknown region according to claim 9 is interpolated. Interpolation method to do. When the lens to be interpolated is a positive intensity lens, the region where the optical performance is unknown is a near-use region, and the optical performance of the region where the progressive power lens is unknown according to claim 9 is interpolated. Interpolation method to do.