JP2024061155A - Spectacle lens design method and spectacle lens designed by said design method - Google Patents

Abstract

[Problem] To provide a method for designing eyeglass lenses that can easily calculate the position of the fovea and obtain the optical performance of the lens based on the visual axis, and to provide eyeglass lenses designed by such a design method. [Solution] A simulation is performed by a computerized eyeball model and a lens placed in front of the eyeball model to transmit light rays, data on the eyeball model's eye axis is obtained, data on the eyeball model's position is calculated using the data on the eye axis, and the optical performance of the lens is obtained based on the obtained data on the fovea position and light passing through the visual axis connecting the nodal points, thereby designing an asymmetrical lens that is not rotationally symmetric. [Selected Figure] Figure 7

Description

The present invention relates to a method for designing eyeglass lenses and eyeglass lenses designed using the same design method.

In designing eyeglass lenses, when ray tracing is used to simulate lens characteristics such as power and aberration using a computer device, this has traditionally been done on the assumption that light rays pass through the eye's center of rotation. The eye's center of rotation is the center of rotation of the eyeball and the point through which the "ocular axis" passes. However, in reality, the line of sight when looking at an object does not pass through the eye's center of rotation. The axis through which the line of sight passes is called the "visual axis," and this visual axis passes through the fovea centralis, where visual acuity is strongest. The fovea centralis is located at the center of the macula of the retina and contributes to vision in the central field. To be precise, the fovea centralis is not located on the optical axis, but is shifted 4 to 8 degrees toward the ear from the optical axis, and on average is shifted 5.5 degrees toward the ear (1 degree downward). Patent Document 1 is shown as prior art regarding the fovea centralis.

JP 2020-106599 A

The reason why the eye axis was used as the reference in conventional simulations is that it is advantageous in terms of calculation because the eye rotation center, which is the center of rotation of the eyeball model, can be used as the origin for calculations, but also because the difference between the visual axis and the eye axis was not considered very strictly, and it was considered sufficient as a method for obtaining lens characteristics even if it was assumed that the eye rotation center was on the line of sight. On the other hand, when the visual axis is used as the reference, the position of the fovea must be calculated, which is computationally cumbersome. Furthermore, when the axial length is used as a parameter to calculate the position of the fovea, the calculation becomes even more complicated.
However, in recent years, eyeglass lenses have come to require customized optical characteristics according to the user's vision, and more accurate optical performance is desired. Therefore, simulations based on the visual axis are once again required in the design and evaluation of eyeglass lenses, and a method is required to easily calculate the position of the fovea and obtain lens characteristics based on the visual axis. There is also a demand for eyeglass lenses designed with such a design concept and manufactured based on the obtained processing data.
The present invention has been made in consideration of the problems existing in the conventional technology as described above. The purpose of the present invention is to provide a method for designing a spectacle lens that can easily calculate the position of the fovea and obtain the optical performance of the lens based on the visual axis, and a spectacle lens designed by such a design method.

As a first means for solving the above problem, a simulation is performed using a co-computer device to transmit light rays through an eyeball model and a lens placed in front of the eyeball model, data on the ocular axis of the eyeball model is obtained, and position data of the fovea in the eyeball model is calculated using the data on the ocular axis. The optical performance of the lens is obtained based on the obtained position data of the fovea and light rays passing through the visual axis connecting the nodal points, thereby designing an asymmetric lens that is not rotationally symmetric.
This allows accurate calculation of foveal position data using clear data on the eye axis as position information, so that the optical performance of the lens can be obtained based on the calculated foveal position data and the light passing through the visual axis connecting the nodal points. Then, based on the foveal position data, it is possible to obtain an asymmetric lens in which the temporal region and the nasal region are not rotationally symmetrical with respect to the fovea, which provides more accurate lens optical performance for the user.

"Optical performance of a lens" refers to the lens performance (characteristics) used in existing lens evaluations, such as S power, C power, spherical equivalent power (S+C/2), cylindrical power and its axis degree, prism amount and its base value, addition power in progressive power lenses, astigmatism, distortion aberration, power error, etc., and these performance characteristics can be used alone or in combination for design and evaluation.
As the "eyeball model", for example, data of an actually measured eye, such as a Gustrand eye model, may be used, or the center of eye rotation may be simply set at a position about 24 to 29 mm away from the rear surface of the lens. The distance from the rear surface of the lens to the center of eye rotation is long in cases such as axial myopia, and also varies when the lens position changes depending on the height of the nose, so it is preferable to set it according to the conditions to be simulated.
The "ocular axis" is the straight line axis that passes through the center of eye rotation and the nodal point of the eyeball.
The "visual axis" is the straight line axis passing through the fovea and nodule on the retina of the eye.
In the simulation, the gaze point becomes the emission point of the point light source in ray tracing, and the simulation is performed with every point on the lens as the gaze point. The obtained optical characteristics are supplemented by interpolation calculations as necessary.

"A lens that is not rotationally symmetrical and asymmetrical" does not include a lens that is asymmetrical and has a lens power with an astigmatism axis in an oblique direction, such as C 1.00 AX45, and is therefore rotationally symmetrical. The center of rotation of the rotational symmetry is the geometric center. The axis of symmetry that serves as the basis for left-right symmetry and asymmetry may be, for example, a vertical line passing through the geometric center.
The position of the fovea is shifted 4 to 8 degrees toward the ear from the optical axis. In other words, when the optical performance of the lens is obtained based on the light passing through the visual axis and the lens is manufactured, the shift is reflected, so the optical performance of the single-focus lens is not symmetrical. "Not symmetrical" means that, assuming an S power without astigmatism in a single-focus lens, the power changes concentrically from the center if the calculation is based on the eye axis, and is symmetrical at least with respect to the optical axis (eye axis) passing through the center of the lens, but in the present invention, the power of the left and right points that are equidistant from the center with the visual axis passing through the center of the lens as the reference is different. Since the fovea is shifted toward the ear, the shift is larger when the line of sight is turned inward than when it is turned outward. As a result, the lens power tends to be stronger on the nose side than on the ear side at points that are equidistant on the left and right with respect to the visual axis passing through the center of the lens as the reference.
In addition, when the position of the fovea is shifted and the image becomes asymmetrical with respect to the optical axis (ocular axis) passing through the center of the lens, it is advisable to use different aspheric coefficients on the nose side and the ear side. The aspheric coefficient is a coefficient that indicates the amount of deviation from the spherical sag at a position that is a radius r away from the origin (e.g., the geometric center of the lens). When the variable in the term of the formula expressing the aspheric coefficient is multiplied by the fourth power of the radius, for example, it is called a fourth-order aspheric coefficient.

As a second means, the visual axis is calculated based on the deviation of the axial angle between the eye axis and the visual axis.
Both the visual axis and the eye axis pass through the nodal point, but while the eye axis passes through the center of eye rotation, the visual axis does not. Therefore, it is possible to calculate the position data of the fovea by applying the coordinates on the eye axis according to the difference in the angle between the two. The angle of the visual axis with respect to the eye axis is shifted to the ear side and downward, respectively, with the angle on the ear side being the larger shift. Therefore, it is better to perform calculations taking into account at least the angle on the ear side.
As a third means, a gaze point is set on a two-dimensional plane at an arbitrary viewing distance through which the visual axis passes, and the position where the upper axis passes on the two-dimensional plane when the visual axis passes through the gaze point is set as an intersection point, the amount of eye rotation is calculated based on a ray directed from the intersection point toward the center of eye rotation, and position data of the fovea is calculated based on the calculated amount of eye rotation.
This is a method for calculating more specific foveal position data. In other words, since the coordinates are clear if the data is based on the eye axis, the fixation point through which the visual axis passes is set on a two-dimensional plane, and the intersection point where the eye axis corresponding to the visual axis connects on the two-dimensional plane is used. This makes it possible to calculate the amount of rotation of the eyeball model when the visual axis faces the line of fixation by applying the amount of eye rotation based on the eye axis.
The "ray of light heading from the intersection toward the center of rotation of the eye" coincides with the axis, and if there is no lens, it will be a straight line, but if there is a lens, it will be refracted at the lens surface and head toward the center of rotation of the eye.

As a fourth means, the calculated amount of eye rotation is applied to a third intersection point that passes through the eye axis and intersects with the eyeball model to calculate position data of the fovea.
The third intersection point is a virtual point on the retina. Since the fovea is also a point on the retina, the accurate fovea on the visual axis can be calculated by applying the amount of eye rotation to the third intersection point on the eye axis according to the angle of deviation between the eye axis and the visual axis.
As a fifth means, the amount of eye rotation is calculated in a state where the lens is placed in front of the eyeball model.
As can be seen from this method, it is possible to calculate the fovea on the visual axis based on the data of the eye axis even without placing the lens to be designed. However, due to the influence of the refractive power and aberration of the lens, the actual position of the fovea will be slightly shifted compared to when the lens is not placed. Therefore, in order to obtain greater accuracy, it is better to perform the calculation with the lens to be designed placed in front of the eyeball model.

As a sixth means, a rotation matrix according to the amount of rotation is obtained when calculating the amount of eye rotation, and the position data of the fovea is calculated based on the rotation matrix.
The best method for calculating the amount of eye rotation, which is a three-dimensional coordinate movement, is to obtain a rotation matrix. This makes it possible to apply the amount of movement of coordinates on the eye axis to coordinates on the visual axis. As for the rotation matrix, since the eyeball model uses the eye axis that passes through the eye rotation center as the rotation axis, it is good to use, for example, the "Rodriguez rotation matrix" to make the calculation of the amount of eye rotation more efficient.
As a seventh means, the calculation based on the deviation of the axial angle between the eye axis and the visual axis is performed using different parameters depending on the eye axis length.
Since the angle between the eye axis and the visual axis varies depending on the axial length, it is advisable to calculate the angle using the axial length as a parameter. In particular, since the deviation angle of the visual axis from the eye axis toward the ear is large, it is advisable to adjust the deviation angle.
For example, it is preferable to use an angle corrected by taking into account the axial length using the following formulas 1 and 2. In formula 1, L is the average axial length, and Δ is the amount of change in the axial length. SR in formula 2 is the prescribed spherical power of the wearer, and refers to a measured value obtained by an optometer such as an autoreflex or a phoropter. Note that applying formula 1, which uses the axial length as a parameter, is preferable because it takes into account the individual eyeball model more than formula 2, which simply takes into account the prescribed spherical power.

In addition, as an eighth means, a left-right asymmetric single-focus eyeglass lens in which the ear-side region and the nose-side region are not rotationally symmetrical is provided, which is designed by the eyeglass lens design method of any one of the first means to the eighth means.
Based on the lens shape data designed by the above design method, it is possible to produce a left-right asymmetric single-focus eyeglass lens in which the ear side region and the nose side region are not rotationally symmetric. The lens shape data is shape data according to the lens power applied to the front or back surface of the lens, and eyeglass lenses with the lens power of any user are produced based on the shape data. The eyeglass lens may be obtained by cutting or grinding the front or back surface of a semi-finished blank, which is a transparent block body made of glass or resin material, with a processing tool to obtain a precursor lens (so-called round lens), or by molding the lens mold of an eyeglass lens and molding it with resin. In the following, lenses in these precursor lens states are referred to as eyeglass lenses. The reason why they are referred to as precursor lenses is that actual eyeglass lenses are generally processed to match the frame shape and are then made into a so-called edged state. In other words, eyeglass lenses are considered to be eyeglass lenses whether or not they are edged. Examples of processing tools include NC lathes, CAD/CAM devices, etc. Processing data can be input into these devices and the computer can be controlled by a program to perform processing. The lens mold can also be processed by CAD/CAM devices, etc. The machining data is generally sag data that determines the cutting amount based on a reference point.

As a ninth aspect, a lens is evaluated based on the optical performance of the lens obtained by a computer simulation that evaluates the optical performance of the lens based on the optical performance acquired by the eyeglass lens design method according to any one of the first to eighth aspects. In the present invention, for example, a designer at an eyeglass manufacturer carries out the design, and the lens designed by the designer is evaluated.
In the present invention, for example, a designer at an eyeglass manufacturer carries out the design and evaluates the lenses.
The present invention is not limited to the configurations described in the following embodiments. The components of each embodiment and modification may be arbitrarily selected and combined. Any component of each embodiment or modification may be arbitrarily combined with any component described in the Summary for Solving the Problems of the Invention or any component that embodies any component described in the Summary for Solving the Problems of the Invention. The present invention also intends to obtain rights to these by amending the present application or filing a divisional application, etc.
In addition, the applicant intends to obtain rights to the overall design or partial design by filing a conversion application to a design application. The drawings show the entire device in solid lines, but they also include partial designs claimed for a portion of the device as well as the overall design. For example, a partial design may include a portion of the device as a partial design, regardless of the portion. A portion of the device may be a portion of the device, or may be a part of that portion.

In the present invention, since the position data of the fovea can be accurately calculated using clear data on the eye axis as position information, the optical performance of the lens can be obtained based on the calculated position data of the fovea and the light rays passing through the visual axis connecting the nodal points. Based on the position data of the fovea, it is possible to obtain an asymmetric lens in which the temporal and nasal regions are not rotationally symmetrical with respect to the fovea, providing more accurate optical performance for the lens according to the user.

FIG. 2 is a block diagram for explaining an electrical configuration of the embodiment. FIG. 13 is an explanatory diagram illustrating a visual axis directed toward a specified gaze point on a screen in a simulation of an embodiment, and the intersection point on the screen to which the eye axis is directed at that time. FIG. 11 is an explanatory diagram for explaining calculation conditions when determining an intersection in a simulation according to an embodiment. Schematic diagram for explaining the rotational movement of an eyeball model according to Listing's law. 13A and 13B are diagrams illustrating the rotation state of the eye axis when looking from the front toward a specified gaze point in a simulation of an embodiment. 11A and 11B are explanatory diagrams illustrating the relationship between the eye axis, the intersection point, and the designated gaze point in a simulation according to an embodiment. FIG. 13 is an explanatory diagram for explaining the direction of light rays when determining the foveal position when the visual axis is directed toward a specified gaze point in a simulation of the embodiment. FIG. 13 is an explanatory diagram for explaining the arrangement of a plurality of starting points of secondary rays at a predetermined angle on a circumference around a principal ray in a simulation of an embodiment. (a) to (c) are schematic diagrams to explain that the visual axis passing through the fovea passes through different positions on the lens on the nasal and temporal sides. 1 is a graph showing the results of a simulation of visual acuity distribution for a conventional eyeglass lens based on eye rotation and the eyeglass lens of Example 1 based on the fovea. 11 is a graph showing the results of a simulation of visual acuity distribution for a conventional eyeglass lens based on eye rotation and an eyeglass lens of Example 2 based on the fovea.

Specific embodiments will be described below.
(Embodiment)
1 is a schematic block diagram of an example of a computing computer 1 for implementing the design method of the present invention. The computing computer 1 is connected to a monitor 2 and a printer 3 as display means or output means, and an input device 4 such as a keyboard and a mouse.
The arithmetic computer device 1 is composed of a CPU (Central Processing Unit) 5 and peripheral devices such as a storage device 6. The CPU 5 executes processing based on various programs in response to commands from the input device 4. The storage device 6 stores basic programs such as a program for controlling the operation of the CPU 5 and an office automation processing program for managing functions that can be commonly applied to multiple programs (e.g., a Japanese language input function, a printing function, etc.).
The storage device 6 also stores a simulation program that performs simulations of back surface ray tracing and transmitted light ray tracing along the visual axis based on lens shape data, and a simulation program that performs simulations of visual acuity based on optical performance data obtained as a result of ray tracing.
The CPU 5 also stores in the storage device 6 shape data for the lens to be designed, and optical performance data calculated as a result of executing simulations of back surface ray tracing and transmitted light ray tracing for the lens with shape data.
Furthermore, the CPU 5 executes a simulation in accordance with a calculation program stored in the storage device 6, and creates an average power distribution chart, an astigmatism distribution chart, a prism distribution chart, a distortion distribution chart, etc. based on the obtained data, and outputs them from the monitor 2 or the printer 3.
It should be noted that the following calculations do not necessarily have to be performed by a single computing computer device 1, and may be performed by one computing computer device 1 based on the results of calculations performed by another computing computer device 1.

Next, a specific example of the calculation of the visual axis and the simulation by tracing rays passing through the visual axis, which are executed by the simulation software of the computing computer device 1, will be specifically described with reference to Figures 2 to 7. Note that, although the deviation angle between the visual axis and the eye axis is actually very small, in the following explanation using the figures, the deviation angle between the visual axis and the eye axis is exaggerated to make it easier to understand.
In reality, the deviation angle between the visual axis and the eye axis is very small, but in the explanation using the figures below, the deviation angle between the visual axis and the eye axis is exaggerated to make it easier to understand.
Here, we will simulate using a single-focus lens, and assume that the center of an object at infinity (for example, 10 m) is viewed with both eyes through the eyeglass lenses. Of course, simulation using one eye is also possible.

A. Calculation of the intersection point with respect to the designated gaze point As shown in Fig. 2, in this embodiment, a designated gaze point T is set (assumed) on a screen assumed to be at a position of an arbitrary viewing distance as the direction of the visual axis. If the visual axis is directed toward the designated gaze point T, the eye axis corresponding to the visual axis will also pass through the screen, so in the simulation, the intersection point (Pr, Pl) between the left and right eye axes and the screen is calculated.
(1) Calculation Conditions The calculation conditions are explained with reference to Fig. 3. At this stage, calculations are performed assuming no lens. The direction of light travel is the X coordinate, the vertical direction perpendicular to this is the Y direction, and the horizontal direction of the screen is the Z coordinate.
As shown in Figure 2, the designated gaze point T is set to (Z0, Y0) (unit: mm). The visual distance (distance from the interpupillary midpoint to the designated gaze point T) is set to a fixed value of D [mm]. Using the interpupillary midpoint as the reference, the Z coordinate (Kz) of the ocular rotation center for each eye is set to Kz = -PD/2 [mm] for the left eye and Kz = +PD/2 [mm] for the right eye (PD is the designated interpupillary distance). The ocular rotation center K is assumed to be a point on the horizontal line that includes the interpupillary midpoint.

(2) Calculation method (the calculation method is the same for the right eye and the left eye)
a) Eye rotation follows Listing's law, which states that "the rotation of the eyeball when the gaze is directed to a certain third eye position (diagonal direction) is uniquely determined by rotating the eye rotation axis (Listing rotation axis) perpendicular to the plane (Listing plane) that includes the gaze of the first eye position (front) and the third eye position." (As shown in Figure 4) In the Listing plane according to Listing's law, the first eye position vector is the front gaze direction, and the third eye position vector is the eye rotation direction. The first eye position vector is G1 (1,0,0), and the third eye position vector is G3 (qx, qy, qz). These are unit vectors.
According to Listing's law, the vector I of the Listing rotation axis can be calculated as the cross product of G1 and G3. That is,
I = G1 x G3
The eye rotation angle θi of such a Listing rotation axis is calculated by the following formula 3.

Using this eye rotation angle θi, we calculate Rodrigues rotation matrix L as an eye rotation matrix that follows Listing's law. Rotation matrix L is shown in the following formula 4. Formula 4 shows the elements of vector I as (dx, dy, dz).

b) Based on the front view in Figure 3, the three-dimensional coordinates of node N are set as N = (Nx, Ny, Nz). If the distance from the center of eye rotation, which is the origin, to the node is, for example, 5.6 mm, node N is N = (5.6, 0, 0). The intersection T0 = (D-Nx, 0, 0) of the eye axis and the screen is determined with node N as the origin, and based on the deviation angle (α, β) of the visual axis relative to the eye axis, the coordinates are transformed to T0' by rotating α around the Y axis and β around the Z axis. Then, as shown in Figures 5 (a) and (b), the difference (ΔZ, ΔY) between the Z and Y coordinates of points T0 and T0' is calculated. ΔY, ΔZ, and T0' are defined by the formula 5. When the visual axis faces any gaze point, the deviation amount between the visual axis on the screen and the eye axis is always assumed to be ΔY and ΔZ. However, when it is anticipated that this assumption may not hold, it is possible to appropriately correct the portion where this assumption does not hold.
From the specified gaze point T = (Z0, Y0) and the difference (ΔZ, ΔY), the intersection point P (Pr, Pl) = (Px, Py, Pz) of the eye axis and the screen when the visual axis with the eye rotation center as the origin points toward the gaze point T can be calculated based on the following formula 6.
The signs of the coordinates such as α, β, ΔZ, ΔY, Z0, Y0, Py, and Pz are appropriately changed depending on how the coordinate system of FIG. 5 is defined.

B. As shown in Figure 6, the direction of the eye axis from the center of eye rotation toward the intersection, that is, the third eye position vector, is clear. The third eye position vector is (Y0-ΔY)/D in Y coordinates and ((Z0-Kz)-ΔZ)/D in Z coordinates. Figure 6 illustrates the relationship between the eye axis and the visual axis on the Z coordinate side. Here, the node is coordinate-converted from N to N' according to Listing's law based on the light ray emerging from the rear surface of the lens when the eye axis faces the intersection. With the lenses to be designed or evaluated worn on the left and right eyes, the amount of eye rotation is obtained as a rotation matrix L from the first eye position vector G1 when looking straight ahead and the third eye position vector G3 based on the light ray emerging from the rear surface of the lens, assuming that the light ray emerges toward the eye rotation from the intersection (Pr, Pl) whose coordinates were calculated in A. Here, θi is calculated again based on the above formula 3, and an arbitrary coordinate P in a three-dimensional space with the eye rotation as the origin is converted to coordinate P' after rotation in the third eye position direction. That is, it is expressed as the following formula 7. The rotation matrix L is the Rodrigues rotation matrix L in the above formula 4.

The initial fovea (Fr, Fl) is coordinate-transformed using the rotation matrix L obtained in C.B. This determines the fovea (Fr', Fl') when the visual axes of the left and right eyes are directed toward the gaze point T. This transformation is calculated as follows. Here, the calculation is performed using the R eye as an example.
a) Assuming the direction of the first eye position, that is, frontal gaze, consider point F0 (16.5,0,0) on the eye axis with the nodal point as the origin. Here, the x-coordinate means the distance from the nodal point to the retina, 16.5 mm. However, when applying formula 2, in order to take into account the deviation Δ from the standard axial length of the wearer, point F0 is defined as (16.5+Δ,0,0) accordingly.
b) As shown in Fig. 2, F0 is subjected to coordinate transformation by the ear-side deviation angle α and the lower-side deviation angle β to obtain the initial foveal position F. The initial foveal position F corresponds to the third intersection point. This calculation is performed according to the following formula 8.
F0 is rotated toward the ear by coordinate transformation (rotation matrix Y(α)) that rotates the Y axis taking into account the deviation angle α, and then F0 is rotated toward the lower retina by coordinate transformation (rotation matrix Z(β)) that rotates the Z axis taking into account the deviation angle β. This is because the fovea is shifted by α toward the ear and β downward with respect to the eye axis based on the nodal point.
In the case of the L eye, the deviation angle α becomes negative, and the sign of sin(α) in the rotation matrix Z(α) changes.

c) As shown in FIG. 7, the initial foveal position F(Fr, Fl) in b) above is coordinate-transformed to the specified third eye position direction using rotation matrix L to obtain the foveal position F'(Fr', Fl') when the visual axis is directed toward the fixation point T. That is, the following formula 9 is used. Rotation matrix L is the Rodrigues rotation matrix L in formula 4 above. At this time, in order to change the origin from the node to the eye rotation point, the distance from the node to the eye rotation point (fixed at 5.6 mm in the embodiment) is subtracted from the x-coordinate at the foveal position F before the coordinate transformation.

Since the position of the fovea (Fr', Fl') when the gaze of the left and right eyes is directed to the gaze point T has been obtained by D.C., the lens power (S, C, AX, Prism/Base, etc.) everywhere in each eye when the gaze point T is looked at is calculated by considering the chief ray going from the gaze point T to the fovea (Fr', Fl') while the lenses to be designed or evaluated are worn in the left and right eyes.
More specifically, a) the chief ray passes through the lens from the gaze point T and reaches the fovea (Fr', Fl'). The incidence angle of the chief ray (the incidence angle from the gaze point to the lens surface) is calculated. At that time, the incidence angle is adjusted taking into account the refraction at the front and back surfaces of the lens so that it reaches the fovea.
b) The secondary rays are set at positions 1.5 mm radius (i.e., the pupil diameter) away from the position of the gaze point of the principal ray at intervals of 2 degrees, and are transmitted through the lens in the same way as the principal ray at the incidence angle of a) above.
c) Calculate the distance (focal length f: unit mm) to the position where the principal ray and at least two secondary rays reach the rear surface of the lens and approach each other to obtain the lens power. The maximum lens power is the S power, and the minimum lens power is the S+C power.

(3) Specific Calculations The above contents a) to c) will be explained in more detail using specific calculation examples.
Based on the prescription's S power, C power, center thickness, and front curve, the back curve of the lens is calculated using the following formula 10. In the following formulas, the back side is represented as Ura and the front side as Omote. Since there is C power, the curve direction is set to two perpendicular directions. In the following vector calculations, the X-axis direction is constant, and only the Y-axis and Z-axis directions change.

Next, the chief ray passing through the fovea after passing through the lens when the visual axis is directed in a certain direction is obtained.
Here, the refracted vector of the light ray after passing through the front surface of the lens is calculated by the vector function formula of the following formula 11, and the refracted vector of the light ray after passing through the rear surface of the lens is calculated by the vector function formula of the following formula 12. In this formula, the incident vector of the chief ray with respect to the lens surface is adjusted so that it passes through the fovea after passing through the lens.

Here, consider the normal vector to be substituted into the above vector function that returns the vector after refraction. The normal vector is expressed as E = (1, Ey, Ez). The normal vector is calculated based on the difference (amount of change) between the sag at the passing point of the ray and the sag at a point that is slightly changed (ΔY, ΔZ) from the passing point. The vector elements Ey and Ez can be expressed as shown in Equation 13 and Equation 14.
The refracted vector Q0mote after passing through the surface is used as a reference during calculation.
The formula for calculating the sag at the lens surface in Equation 13 is expressed by Equation 15. Moreover, the formula for calculating the sag at the lens back surface in Equation 14, which refers to the post-refractive vector Qura after passing through the back surface during calculation, is expressed by Equation 16. The formulas 15 and 16 are sag values that take into account the aspheric sag value (AS) in addition to the basic sag value (sag amount) based on the S power, C power, etc.

The above-mentioned method determines the sag value of the lens with the fovea as the reference for the design lens. A specific eyeglass lens is manufactured based on the sag value. The eyeglass lens with this design is manufactured as an asymmetric lens even if it is a single-focus lens without astigmatism. The reason why a single-focus eyeglass lens designed with the fovea as the reference is asymmetric will be explained.
Equation 17 is an equation that shows the relationship between a certain point on the back surface of a lens and the focal length at that point. Equation 17 is used when performing a ray tracing simulation for the principal ray and the secondary ray based on the refraction vector Qura after passing through the back surface and the point passing through the back surface. This is because secondary rays around the principal ray are required to find the focal length. Specifically, this simulation is performed, for example, as follows.
i) As shown in Fig. 8, multiple starting points of secondary rays are arranged at intervals of angle θ on a circumference of radius r around the principal ray. For example, r = 1.5 mm, θ = 2 degrees. Here, the secondary rays are set to the same incident vector as the principal ray (i.e., parallel to the principal ray), making it easier to calculate the power afterwards.
ii) For a secondary ray in a certain θ direction and a secondary ray 180 degrees opposed thereto, the passing point on the rear surface of the lens and the vector after refraction at the rear surface of the lens are obtained by ray tracing, and the passing point of the principal ray on the rear surface of the lens and the vector after refraction at the rear surface of the lens are also used to calculate the focal length and determine the power according to the following formula 17. Since ray tracing is performed in three-dimensional space, the principal ray is also considered in addition to the two secondary rays to prevent the rays from twisting and deteriorating the accuracy of the focal length calculation.

iii) Execute step ii) above for each θ to find the power for each θ. Then, set the maximum power as the S power, the minimum power as the S+C power, and set the θ at which the power is maximum as the axis of astigmatism.

Again, the coefficient α in equation (17) is expressed by the following equation.
α = luminous flux diameter_ur / (luminous flux diameter_ur - luminous flux diameter_K)
Light beam diameter_ur … Light beam diameter when passing through the rear surface of the lens (Light beam diameter_ur＞0)
Light beam diameter_K: Light beam diameter at point K (center of rotation) after passing through the rear surface of the lens (Light beam diameter_K>0)
As described above, the secondary rays are set to be separated from the principal ray by the radius of the pupil diameter, so in the simulation of the embodiment, the beam diameter is the distance from a point on the lens surface to be evaluated to a position (position of the secondary ray) separated by the radius of the pupil. Therefore, beam diameter_ur and beam diameter_K are calculated as the distance between the principal ray and a pair of adjacent secondary rays. Point K (center of rotation of the eye) is used as the beam diameter because it is advantageous in calculations since its position does not change even if the line of sight is moved.
If the lens has a negative power, α will be a negative value because light flux diameter_ur < light flux diameter_K, and if the lens has a positive power, α will be a positive value because light flux diameter_ur > light flux diameter_K. Also, the greater the difference between light flux diameter_ur and light flux diameter_K, the greater the absolute value of the required lens power.

The light beam diameter_K related to the coefficient α depends on the refraction vector (tanY_ura, tanZ_ura) in the formula (17) of the principal ray after passing through the rear surface of the lens in the lens power calculation formula shown above. In other words, the larger the refraction vector after passing through the rear surface of the lens, the more the light is refracted. For example, in the case of a lens with a negative power, since it is a concave lens, the light after passing through the lens diverges, while in the case of a lens with a positive power, the light converges. The larger the refraction vector, the greater the divergence or convergence.
Based on Figures 9(a) to (c), a simulation is envisaged in which a vertical line (a symmetrical reference line (central line)) passing through the lens geometric center for a single focus lens that will be used for the left eye is used as a reference line, and a certain point on the left and right nose sides and a certain point on the ear sides that are equidistant from the reference line are visually observed.
9(a) and 9(c), the angle of incidence of the light beam on the lens surface is larger when viewing the nose side periphery than when viewing the ear side periphery. When the angle of incidence is larger, the refraction vector of the chief ray after passing through the rear surface of the lens is also larger. When the refraction vector is larger, as described above, in a lens with a negative power, the light after passing through the lens is more divergent and the value of α is smaller. Therefore, in this case, the lens power is relatively larger when viewing the nose side periphery, and as a result, the optical performance is asymmetrical, in which the equivalent spherical power of the ear side region and the nose side region is not rotationally symmetric based on the design with the fovea as the reference.
Here, the degree of left-right asymmetry depends on the shift angle of the fovea relative to the optical axis. As can be seen from Equations 1 and 2, the shift angle varies from person to person, but as mentioned at the beginning, it is generally 4 to 8 degrees, so a shift angle of less than 10 degrees is applied.

With the above-described configuration, the embodiment provides the following effects.
(1) The position of the fovea (Fr', Fl'), whose coordinates are unknown, is found based on the intersections (Pr, Pl) and nodal points or center of rotation of the eye that are clear in terms of coordinates and pass through the eye axis, and the deviation angle. This makes it possible to trace rays using the visual axis, which is the original way of seeing, and thus makes it possible to more accurately verify the user's visual condition.
(2) By performing coordinate transformation using a rotation matrix before calculating the fovea (Fr', Fl'), accurate and optimal calculations can be made for the rotating eyeball model.
(3) By designing an asymmetric single-focus eyeglass lens in which the equivalent spherical power in the ear side and nose side regions is not rotationally symmetric, it is possible to produce a single-focus eyeglass lens with more accurate optical performance tailored to the user based on the fovea.

Below, the results of a simulation of a lens designed according to the method of the present invention, assuming monocular vision, are shown.
Example 1
・R eye S-4.00
・Center thickness CT = 1.1 (mm)
Substrate refractive index n = 1.600
・Table curve 1.15 curve (substrate refractive index conversion)
Surface curvature radius r0 = 1000 (n-1)/1.15 = 521 (mm)
Surface curvature Co = 1/r0 = 0.00191 (mm ^-1 )
・Principal curvature of the inner surface Cx = (1.15 - (-4.00)) / (1000 (n-1))
= 0.00858 (mm ^-1 )
Cy = (1.15 - (-4.00)) / (1000 (n-1))
= 0.00858 (mm ^-1 )
Shift angle: 5.5 degrees as average value. The results of the simulation are shown in FIG. 10. In FIG. 10, the right side shows the characteristics of the eyeglass lens of Example 1 designed based on the fovea of this embodiment, and the left side shows the characteristics of the eyeglass lens based on the conventional eye rotation in the above prescription. The shift angle is 0 degrees in the eyeglass lens based on the conventional eye rotation. Since the eye is the R eye, if the coordinate value on the horizontal axis is negative, it is the nose side, and if it is positive, it is the ear side. FIG. 10 shows the distribution of visual acuity of Example 1 and the conventional example calculated based on the S degree, C degree, and astigmatism axis obtained by simulation. It shows how visual acuity changes from 1.0 from the center to the periphery of the distribution. It can be seen that the visual acuity distribution of Example 1 is improved compared to the conventional example, with a wider area where the visual acuity is close to 1.0 in the center.

Example 2
・R eye S+4.00
・Center thickness CT = 4.5 (mm)
Substrate refractive index n = 1.600
・Table curve 5.97 curve (substrate refractive index conversion)
・Surface curvature radius r0 = 1000 (n-1) / 1.15 = 100 (mm)
Surface curvature Co = 1/r0 = 0.00995 (mm ^-1 )
・Principal curvature of the inner surface Cx = (5.97 - (+4.00)) / (1000 (n-1))
= 0.00328 (mm ^-1 )
Cy = (5.97 - (+4.00)) / (1000 (n - 1))
= 0.00328 (mm ^-1 )
Shift angle: 5.5 degrees as average value The results of the simulation are shown in FIG. 11. In FIG. 11, the right side shows the characteristics of the eyeglass lens of Example 2 designed based on the fovea of this embodiment, and the left side shows the characteristics of the eyeglass lens based on the conventional eye rotation in the above prescription. FIG. 11 shows the distribution of visual acuity of Example 1 and the conventional example calculated based on the S power, C power, and astigmatism axis obtained by simulation. It shows how visual acuity changes from 1.0 from the center to the periphery of the distribution. As with Example 1, it can be seen that the visual acuity distribution of Example 2 is improved compared to the conventional example, with a wider area corresponding to the central visual acuity value close to 1.0.

The above examples are merely described as specific embodiments for illustrating the principles and concepts of the present invention. In other words, the present invention is not limited to the above embodiments. The present invention can be embodied in the following modified forms, for example.
The above embodiment is merely an example. The calculation may be performed in an order other than the above.
In the above specific calculations, in Equations 15 and 16, the sag value is calculated taking aspheric sag into consideration, but the sag value may be calculated using only the basic sag value, and the aspheric sag amount may be calculated separately later and added together. Similarly, in the case of a progressive power lens, the progressive sag amount must be taken into consideration, but like the aspheric sag amount, Equations 15 and 16 may be calculated taking the progressive sag amount into consideration from the beginning, or may be calculated separately later and added together.
In the case of a simulation, the above-mentioned number and positions of secondary rays are merely examples, and calculations may be performed using numbers and positions of secondary rays other than those mentioned above.
Although the above describes an example of a simulation using a single-focus lens, it is also possible to simulate wearing a progressive-addition lens.
In the above embodiment, a calculation method assuming a frontal view has been given as an example for determining the intersection point (Pr, Pl). However, the intersection point (Pr, Pl) may be determined by calculation using a specified gaze point T as a reference point.
The lens to be designed or evaluated in the simulation may be any lens used as a spectacle lens. For example, a spherical lens, an aspherical lens, a progressive power lens, etc. may be used.
In the above, in order to simplify the calculation, average angles are used for the deviation angles α and β. However, the deviation angles α and β may be appropriately changed in accordance with the axial length of the wearer to perform the simulation.

Claims (8)

A method for designing eyeglass lenses, comprising: executing a simulation of transmitting light rays through an eyeball model and a lens placed in front of the eyeball model using a computer device to obtain data on the eyeball model's axial direction; calculating position data of the fovea in the eyeball model using the data on the axial direction; obtaining the optical performance of the lens based on the obtained position data of the fovea and light rays passing through the visual axis connecting the nodal points; and designing an asymmetrical lens that is not rotationally symmetrical. The method for designing eyeglass lenses according to claim 1, characterized in that the calculation of the visual axis is performed based on the angular deviation in the axial direction between the eye axis and the visual axis. The method for designing eyeglass lenses according to claim 2, characterized in that a fixation point is set on a two-dimensional plane at an arbitrary viewing distance through which the visual axis passes, a point of intersection is set at a position where the axis passes on the two-dimensional plane when the line of sight passes the fixation point, the amount of eye rotation is calculated based on a ray directed from the intersection point toward the center of eye rotation, and the position data of the fovea is calculated based on the calculated amount of eye rotation. The method for designing eyeglass lenses according to claim 3, characterized in that the calculated amount of eye rotation is applied to a third intersection point that passes through the eye axis and intersects with the eyeball model to calculate the position data of the fovea. The method for designing eyeglass lenses according to claim 4, characterized in that the amount of eye rotation is calculated with the lens placed in front of the eyeball model. The method for designing eyeglass lenses according to claim 1, characterized in that, when calculating the amount of eye rotation, a rotation matrix corresponding to the amount of rotation is obtained, and the position data of the fovea is calculated based on the rotation matrix. The method for designing eyeglass lenses according to claim 1, characterized in that the calculation based on the deviation in the axial angle between the eye axis and the visual axis is performed using different parameters depending on the axial length. An asymmetric single-focus eyeglass lens in which the ear side region and the nose side region are not rotationally symmetrical, designed by the eyeglass lens design method of claim 1 or 2.