Method for calculating corrective power of eyeglass lens

Abstract

To provide a method for calculating the corrective power of an eyeglass lens that calculates a transmitted-light wearing power on the basis of a visual axis when the lens is fitted into a curved eyeglass frame having a face-form angle and a pantoscopic angle, and calculates a corrective power corresponding to an accurate prescription power on the basis of the transmitted-light wearing power.SOLUTION: The method for calculating corrective power of an eyeglass lens includes the steps of: executing, by a computer device, a simulation of transmitting light rays through an eyeball model and a lens arranged in front of the eyeball model to acquire data on an ocular (optical) axis of the eyeball model; calculating position data of a fovea within the eyeball model using the data on the ocular axis; changing a fixation-point position according to a face-form angle and executing, on the basis of a new fixation point, a simulation to obtain light rays that pass along a visual axis connecting the fovea position data and a nodal point; calculating a transmitted-light wearing power on the basis of the obtained light rays; and calculating the corrective power on the basis of the transmitted-light wearing power.SELECTED DRAWING: Figure 9

Description

[Technical Field]

[0001] The present invention relates to a method for calculating the correction power of an eyeglass lens, which is used to calculate the value of the prescription power that changes when fitting a lens into an eyeglass frame with a large bending angle or forward tilt angle as the correction power. [Background technology]

[0002] In designing eyeglass lenses, ray tracing, for example, when simulating lens characteristics such as power and aberration using computerized equipment, has traditionally been performed under the assumption that light rays pass through the eye's center of rotation. The center of rotation is the center around which the eyeball rotates and the point through which the "ocular axis" passes. However, in reality, when viewing an object, the line of sight does not pass through the 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 central vision. The fovea centralis is not exactly located on the optical axis; it is offset 4 to 8 degrees toward the ear from the optical axis, with an average offset of 5.5 degrees toward the ear (1 degree downward). It is known that the amount of foveal offset varies depending on the axial length of the eye. The reason why the eye axis was used as the reference in conventional simulations is that it is advantageous in terms of calculations because the eye's center of rotation, 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 has not been considered very strict, and so it has been considered sufficient as a method for obtaining lens characteristics even if it is assumed that the eye's center of rotation is 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, if the axial length is used as a parameter when calculating 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 lens optical performance is desired. Therefore, there is a need for simulations based on the visual axis again in the design and evaluation of eyeglass lenses, and for this purpose, there is a need for a method that can easily calculate the position of the fovea and obtain lens characteristics based on the visual axis. Therefore, the applicant developed the invention shown in Patent Document 1. Patent Document 1 describes a method of determining the visual axis using the eye axis in a computer simulation, and obtaining the optical performance of the lens based on that visual axis to design the lens. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-167305 [Patent Document 2] Japanese Patent Application Laid-Open No. 2005-284059 Summary of the Invention [Problem to be solved by the invention]

[0004] Incidentally, in recent years, eyeglass frames that are curved to fit the face have become widely used, mainly in fashionable imported frames and sports sunglasses (hereinafter, for convenience, such eyeglass frames will be referred to as curved eyeglass frames). The degree of curvature of such curved eyeglass frames is generally evaluated by the inclination angle φ of the curved eyeglass frame with respect to a line segment m perpendicular to the eye axis L, as shown in Figure 13. This inclination angle φ is generally called the curvature angle φ. Similarly, there are eyeglass frames that are tilted to have a forward tilt angle φ, as shown in Figure 14. The forward tilt angle φ is the angle between the frame and a perpendicular line perpendicular to the eye axis when the wearer looks horizontally straight ahead. The main problem with fitting lenses to curved eyeglass frames is that the eye axis is misaligned with the lens's optical axis due to the bend angle or forward tilt angle. Typically, eyeglass stores prescribe lens powers with the eye axis and optical axis aligned. However, if lenses prescribed in this state are worn tilted by, for example, the bend angle, the power in the tilted direction becomes more pronounced. This results in overcorrection of the lens power compared to when prescription lenses are worn in a frame with a normal bend angle, resulting in excess C power. Patent Document 2 is an example of a technology for correcting such bend angles. Patent Document 2 discloses a technology for correcting astigmatism (astigmatism) and prism error when fitting lenses to curved eyeglass frames. Even when performing a computer simulation of fitting lenses to such curved eyeglass frames, it is desirable to determine the optical performance of the lenses based on the "visual axis" rather than the "eye axis," as described above. This is because even if the prescription power, curvature angle, forward tilt angle, etc. are the same, by making corrections to suit each individual eye (differences in axial length), it is possible to achieve a more personalized and optimal wearing experience. However, since curved eyeglass frames have a bend angle and a forward tilt angle, when using the "eye axis" to the "visual axis" as a reference, it is necessary to take this into consideration when calculating the transmitted light wearing power and correct the prescribed power. The present invention provides a method for calculating the correction power of eyeglass lenses, which calculates the transmitted light wearing power based on the visual axis when fitting lenses into a curved eyeglass frame with a curvature angle or forward tilt angle, and calculates the corrective power for an accurate prescribed power based on the transmitted light wearing power. [Means for solving the problem]

[0005] As a first means for solving the above problem, a method for calculating the corrected power of an eyeglass lens by computer simulation is provided, in which a lens with a predetermined prescription power is fitted into an eyeglass frame with a curvature angle, and the transmitted light wearing power obtained when the eyeglass frame is worn with the curvature angle is corrected to approach the predetermined prescribed power. The method uses a computer device to perform a simulation in which a light ray passes through an eyeball model and a lens placed in front of the eyeball model and reaches a gaze point, obtains data on the eyeball model's axis, calculates position data of the fovea in the eyeball model using the data on the eyeball axis, changes the position of the gaze point according to the curvature angle, and performs a simulation to obtain a light ray passing through the visual axis connecting the position data of the fovea and the nodal point based on the new gaze point, calculates the transmitted light wearing power based on the obtained light ray, and calculates the corrected power based on the transmitted light wearing power. This allows the transmitted light wearing power to be calculated based on the visual axis rather than the eye axis when fitting a lens with a specified prescribed power into an eyeglass frame with a curvature angle, thereby increasing the accuracy of the transmitted light wearing power value and enabling the correction power for the prescribed power calculated based on this transmitted light wearing power to be accurately obtained.

[0006] "Prescription power" refers to the lens performance (characteristics) for the user, such as S power, C power, spherical equivalent power (S+C / 2), astigmatism power and its axis, prism amount and its base value, addition power in progressive power lenses, astigmatism, distortion, power error, etc. These performance factors can be used alone or in combination for design and evaluation. The "eyeball model" may be, for example, data from an actually measured eye, such as a Gustrand eye model, or the center of rotation may be simply set at a position approximately 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 rotation is longer in cases such as axial myopia, and the distance also varies when the lens position changes due to changes in nose height, so it is preferable to set the distance according to the conditions to be simulated. The "ocular axis" is the straight axis that passes through the center of rotation and the nodal point of the eyeball. The "visual axis" is the straight line axis that passes through the fovea and nodal points on the retina of the eye. In the simulation, the gaze point becomes the point of emergence 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. The "nodal point" is the point on the eye axis between the lens and the rotation of the eye. In the present invention, the "transmitted light wearing power" means a power that changes depending on the angle of curvature when a user wears a lens with a prescribed power in a spectacle frame with a curvature angle.

[0007] As a second means, a method for calculating the correction power of eyeglass lenses by computer simulation is provided for fitting a lens with a predetermined prescription power into an eyeglass frame with a forward tilt angle, and correcting the transmitted light wearing power obtained when the eyeglass frame is worn at the forward tilt angle to approach the predetermined prescription power. The method includes using a computer device to perform a simulation in which a light ray passes through an eyeball model and a lens placed in front of the eyeball model and reaches a gaze point, obtaining data on the eyeball model's axis, calculating position data of the fovea in the eyeball model using the data on the eyeball axis, changing the position of the gaze point according to the forward tilt angle, and performing a simulation to obtain a light ray passing through the visual axis connecting the position data of the fovea and the nodal point based on the new gaze point, calculating the transmitted light wearing power based on the obtained light ray, and calculating the correction power based on the transmitted light wearing power. This allows the transmitted light wearing power to be calculated based on the visual axis rather than the eye axis when fitting a lens with a specified prescribed power into an eyeglass frame with a forward tilt angle, thereby increasing the accuracy of the transmitted light wearing power value and enabling the correction power for the prescribed power calculated based on this transmitted light wearing power to be accurately obtained. In the second means, the terms used are defined in the same way as in the first means.

[0008] Here, the reason why the position of the point of interest is changed when there is a bending angle or a forward tilt angle in the first and second means will be explained. Even if the curvature angle and forward tilt angle are the same, the transmitted light wearing power changes depending on whether or not the misalignment of the visual axis with respect to the fovea is taken into account. Now, assume that the tilt of the lens, as shown in Figure 15(a), results in a tilt angle of θ when the ocular axis is used as the reference. On the other hand, as shown in Figure 15(b), a tilt angle of θ' occurs when the visual axis passing through the fovea and the nodal point is used as the reference. θ and θ' are roughly the same for the same curvature angle (the angle difference is exaggerated in the illustration). However, depending on whether the fovea is misaligned with respect to the ocular axis with respect to the nodal point, the degree of inclination of the visual axis with respect to the ocular axis passing through the center of the eyeball, based on the center of rotation of the lens, changes (the same applies to the forward tilt angle). Therefore, even if the curvature angle and forward tilt angle are the same, if the misalignment of the fovea with respect to the ocular axis with respect to the nodal point is taken into account, the transmitted light wearing power will differ from conventional values, and the required correction power will also change.

[0009] As a third means, the coordinates of the fixation point are transformed by a rotation matrix to change the fixation point to the new fixation point. With this method, a determinant can be easily created in relation to the bend angle and forward tilt angle, and the object can be moved to an accurate position. As a fourth means, the calculation for executing a simulation to obtain a ray passing through the visual axis is performed using different parameters depending on the axial length. The angle between the eye axis and the visual axis varies depending on the axial length, so it is best to calculate the angle using the axial length as a parameter. In particular, since the angle of deviation of the visual axis from the eye axis toward the ear is large, it is best to adjust this angle. For example, it is advisable 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 axial length. In formula 2, SR is the wearer's prescribed spherical power, and refers to the measurement value obtained with an ophthalmoscope such as an autoreflex or phoropter. Note that applying formula 1, which uses axial length as a parameter, is preferable because it takes into account the individual's eyeball model more closely than formula 2, which simply takes into account the prescribed spherical power.

[0010]

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[0011]

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[0012] In addition, as a fifth means, a differential power, which is the difference between the specified prescribed power and the transmitted light wearing power calculated based on the new gaze point, is calculated, and the correction power is calculated based on the difference between the target power and the differential power. This calculation allows the correction power of the target power to be calculated for a given prescribed power. The "target power" is a power that can be set arbitrarily to determine how close the vision should be to the prescribed power, with the prescribed power being 100%. The present invention is not limited to the configurations described in the following embodiments. The components of each embodiment and variation may be arbitrarily selected and combined. Furthermore, any component of each embodiment or variation may be arbitrarily combined with any component described in the Summary of the Invention or any component embodying any component described in the Summary of the Invention. The present invention also intends to obtain rights to these by amending this application or filing a divisional application, etc. Furthermore, the applicant intends to obtain rights to the overall design or partial design by filing a conversion application to a design application. The drawings depict the entire device in solid lines, but they also include partial designs claimed for parts of the device. For example, a partial design may be a partial design for a part of the device, or a partial design may be included for a part of the device regardless of the part. A partial design may be a part of the device, or a part of that part. [Effects of the Invention]

[0013] In the present invention, when a lens with a specified prescription power is fitted into an angled eyeglass frame, the transmitted light wearing power can be calculated based on the visual axis rather than the eye axis, thereby increasing the accuracy of the transmitted light wearing power value and enabling accurate correction powers to be obtained for the prescribed power calculated based on this transmitted light wearing power. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 2 is a block diagram illustrating an electrical configuration of the embodiment. [Figure 2] FIG. 10 is an explanatory diagram illustrating the visual axis directed toward a specified gaze point on the screen and the intersection point on the screen toward which the eye axis is directed in the simulation of the embodiment. [Figure 3] FIG. 10 is an explanatory diagram illustrating calculation conditions when determining an intersection point in a simulation according to an embodiment. [Figure 4] Schematic diagram for explaining the rotational movement of an eyeball model according to Listing's law. [Figure 5] 10A and 10B are explanatory diagrams illustrating the rotation state of the eye axis when looking from the front toward a designated gaze point in a simulation of an embodiment. [Figure 6] 10A and 10B are explanatory diagrams illustrating the relationship between the eye axis, the intersection point, and the designated gaze point in the simulation of the embodiment. [Figure 7] FIG. 10 is an explanatory diagram illustrating the direction of light rays when determining the foveal position when the visual axis is directed toward a specified gaze point in a simulation according to an embodiment. [Figure 8] FIG. 10 is an explanatory diagram for explaining that a plurality of starting points of secondary rays are arranged at predetermined angles on a circumference around a principal ray in a simulation of an embodiment. [Figure 9] Schematic diagram illustrating how the gaze point shifts when there is a warp angle. [Figure 10] 10 is a graph showing the results of simulating the calculated values ​​of the spherical equivalent power when the line of sight is moved from the center of the lens onto the horizontal axis. [Figure 11]This table shows the results of a simulation of the difference in equivalent spherical power due to differences in the fovea at the center of the lens, at 16 mm on the ear side and 16 mm on the nose side, as well as at each of the aforementioned points on the ear side and nose side relative to the center of the lens. [Figure 12] 10 is a table showing the relationship between the difference in power at a predetermined point on the side and ear side and the correction rate of the target power. [Figure 13] An explanatory diagram showing the definition of a sway angle using a frame in which the sway angle is defined. [Figure 14] An explanatory diagram showing the definition of sway angle using a frame with a forward lean angle. [Figure 15] (a) is an explanatory diagram that explains the tilt that occurs when the lens is tilted and the eye axis is used as the reference point, and (b) is an explanatory diagram that explains the tilt that occurs when the lens is tilted and the visual axis is used as the reference point. DETAILED DESCRIPTION OF THE INVENTION

[0015] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a specific embodiment of the method for calculating the correction power of a spectacle lens according to the present invention will be described with reference to the accompanying drawings. 1. Overview of calculations for fitting lenses into frames with curvature In this embodiment, it is assumed that the correction power is calculated by accessing the manufacturer's homepage via the Internet from values ​​measured at an eyeglass retailer (user side). As shown in FIG. 1, the Internet is a large-scale communication network in which a plurality of LANs (Local Area Networks) 10 are connected via communication lines such as telephone lines. The eyeglass retailer is equipped with a terminal computer 11. The terminal computer 11 is a WWW (World Wide Web) client connected to the Internet. The terminal computer 11 is an information processing device with a normal hardware configuration that can execute programs in response to user input, and its built-in hard disk is pre-installed with various programs such as a browser and an OS (Operating System) required for using the WWW. Each program is controlled by a CPU (Central Processing Unit) within the terminal computer 11. An input device 12 (mouse, keyboard, etc.) and a monitor 13 are connected to the terminal computer 11. As shown in Figure 1, the manufacturer has a server 15 connected to the Internet. Server 15 is a computer device with a normal hardware configuration that can load programs into memory and execute them in response to external instructions, and its built-in hard disk is installed with software such as httpd (Hyper Text Transfer Protocol Daemon), which receives requests via a browser and provides available files to the browser, a CGI (Common Gateway Interface) script that processes data from httpd, a correction power calculation program started by the CGI script, an OS, etc. Each program is controlled by a CPU (Central Control Unit) within server 15.

[0016] The manufacturer's homepage provides an input and correction result display form (not shown). The user operates the terminal computer 11 to launch a browser on the monitor 13, enters the URL (Uniform Resource Locator) of a specific manufacturer's site, and calls up the manufacturer's web page, which is displayed on the monitor 13. The user uses the input device 12 to input data such as the prescribed S power, C (astigmatism) power, astigmatism axis, prism value, prism base (base direction), and lens base curve into the input and correction result display form. The user also inputs data such as the angle of forward tilt, the angle of curvature, the frame curve, the interpupillary distance (PD), and the axial length. Based on the data sent by the user, the input data is sent to the server 15. The server 15 receives this data and causes a CGI script to execute a correction power calculation program. In this embodiment, the correction power calculation program uses the above input data as parameters to calculate the S power, C power, astigmatic axis AX, prism power P, and prism base B as transmitted light wearing power. Each element is found by substituting the above parameters into its own unique calculation formula. In other words, each element is expressed by the following function. D=F{P,Q,R,S,T...} D: Values ​​corrected by the correction power calculation program for each element P, Q, R, S, T...: Input lens condition data, power prescription data, data related to the curvature angle, data related to the forward tilt angle, etc. The input and correction result display form displays the results of the correction power calculation program executed by the CGI script, including the transmitted light wearing power, corrected prescription value, and corrected wearing power for S power, C power, astigmatism axis AX, prism power P, and prism base B. The correction power calculation program includes 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, and calculates transmitted light wearing power through the simulations.

[0017] Since the actual calculation formula is very complicated, the calculation method will be outlined below. First, we will explain the method for calculating the transmitted light wearing power. The transmitted light wearing power is calculated by calculating what power the light entering the eye will feel when the input prescription power is worn with a lens at a specified bend angle θ (this calculation is called the calculation of transmitted light wearing power). When calculating the transmitted light wearing power, the transmitted light wearing power is calculated by adding an additional power corresponding to the bend angle. For example, to calculate the S power in the transmitted light wearing power, the additional power ΔS amount is calculated based on the value of a specified parameter and added to the prescribed S power. Additional powers are calculated similarly for C power, astigmatism axis, prism power, and prism base other than S power, and the value obtained by adding the additional power to the prescribed power is displayed in the specified field of the input and correction result display form. The S power, C power, astigmatism axis, prism power, and prism base, which are the basis for calculating the transmitted light wearing power, are calculated based on the axial length rather than the ocular axis, so the fovea is calculated based on the ocular axis, and the S power, C power, astigmatism axis, prism power, and prism base are calculated based on the obtained visual axis.

[0018] Next, we will explain the calculation method for the correction power based on the transmitted light wearing power.We consider the transmitted light wearing power in the above-mentioned bend angle to be a state in which extra power is added to the prescribed power, subtract the added power, and then calculate what the transmitted light wearing power will be at that bend angle after subtraction.Specifically, the calculation is performed using the following calculation process. (1) Calculation of transmitted light power First, when the input curvature angle θ degrees is used, a simulation is performed to calculate what power the light entering the eye will feel when wearing a lens with the input prescription power (S power S, C power C, astigmatism axis AX, prism value P, base B). Here, the prescribed power uses the visual axis rather than the eye axis, as mentioned above. Calculations using the visual axis rather than the eye axis will be discussed later. In other words, based on the input axial length and prescribed power, the deviation angle of the fovea from the optical axis in both the horizontal and vertical directions is calculated, and a simulation of the spectacle lens taking the fovea into account is performed to obtain power data for the S power S, C power C, astigmatism axis AX, prism value P, and base B. At this time, the effect of the deviation of the visual axis passing through the fovea due to the lens tilt based on the "curvature angle" and "forward tilt angle" is also taken into account. These calculations will be discussed in detail in "2. Calculation of transmitted light wearing power taking the fovea into account" below. (2) Calculation of differential frequencies Subtract the input prescription power from the transmitted light wearing power obtained in calculation (1). In other words, the process involves finding the composite lens power that cancels out the input prescription power against the transmitted light wearing power. The powers obtained for each element here are called the differential powers (S0, C0, AX0, P0, B0). (3) Setting a target frequency The target power (target Sp for S power, target Cp for C power, target AXp for astigmatism axis, target Pp for prism, and target Bp for base) is set from the "input prescription power" and "difference power" taking into account the correction rate and the design of the lens periphery. For example, when the correction rate is 100%, the "target power" and the "input prescription power" will be equal. Alternatively, when the correction rate is uniformly 60%, a difference power of 40% is allowed, so the target power is calculated by adding the "difference power" x (1 - 0.6) to the "input prescription power."

[0019] (4) Calculation of corrected power 4-1: Subtract the "difference power" from the "target power." The power obtained here is the provisional correction power. In other words, a lens that cancels out the difference power (S0, C0, AX0, P0, B0) is synthesized with the target power (Sp, Cp, AXp, Pp, Bp) to obtain the provisional correction power (S1, C1, AX1, P1, B1). 4-2: When the input bend angle is θ degrees, the transmitted light wearing power when wearing the lens with the "provisional correction power" is calculated following the calculation in the first display field 33a. The power obtained by this calculation is the corrected wearing power. Regarding this "corrected wearing power", (i) If it is determined that the power is close to the "target power," the corrected wearing power obtained in 4-2 is displayed as a result in the second display field 33b. (b) If the difference from the "target power" is judged to be large, subtract the "target power" from the "corrected wearing power." The power obtained here is then used as the second difference power. 4-3: Subtract the "second difference power" from the "provisional correction power." Then, use the obtained power as the new "provisional correction power" and return to the beginning of 4-2 to calculate the transmitted light wearing power. If it is (a), stop at that stage. If it is (b), return to the beginning of 4-2 and repeat the calculation (converge) until it becomes (a).

[0020] 2. Calculation of transmitted light wearing power taking the fovea into account Next, an example of a method for calculating the transmitted light wearing power obtained by the calculation in 1 above will be explained in detail with reference to Figures 2 to 7. Here, on the premise that the input prescription power is based on the axial length, a simulation is performed to find the fovea based on the input axial length, and a simulation is performed for a gaze point that has moved (shifted) according to the curvature angle based on the fovea to calculate the transmitted light wearing power. In reality, the angle of deviation between the visual axis and the eye axis is very small, but in the explanation using the following figures, the angle of deviation 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.

[0021] A. Calculation of the intersection point for the specified gaze point As shown in Fig. 2, in this embodiment, a designated gaze point T is first 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 that 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 found. (1) Calculation conditions The calculation conditions are explained based on Figure 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 specified gaze point T is set to (Z0, Y0) (unit: mm). The visual distance (distance from the interpupillary midpoint to the specified gaze point T) is set to a fixed value of D [mm]. Using the interpupillary midpoint as the reference point, 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 specified interpupillary distance). The ocular rotation center K is assumed to be a point on the horizontal line that includes the interpupillary midpoint.

[0022] (2) Calculation method (the calculation method is the same for the right and left eyes) a) Eye rotation follows Listing's law, which states that "the rotation of the eyeball when directing the gaze 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) containing 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×G3 The eye rotation angle θi of such a Listing rotation axis is calculated by the following formula 3.

[0023]

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[0024] Using this eye rotation angle θi, the Rodrigues rotation matrix L is calculated as an eye rotation matrix according to Listing's law. The rotation matrix L is shown in the following equation 4. Equation 4 shows the elements of vector I as (dx, dy, dz).

[0025]

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[0026] 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 rotation of the eye (the origin) to the node is, for example, 5.6 mm, then node N is N = (5.6, 0, 0). The intersection point T0 = (D-Nx, 0, 0) of the eye axis and the screen is determined, with node N as the origin. Based on the deviation angle (α, β) of the visual axis relative to the eye axis, coordinate transformation is performed to T0' by rotating α around the Y axis and β around the Z axis. Then, as shown in Figures 5(a) and 5(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 Equation 5. When the visual axis is directed toward any point of gaze, the deviation amount between the visual axis on the screen and the eye axis is always assumed to be ΔY and ΔZ. However, if it is anticipated that this assumption will not hold, it is possible to make appropriate corrections to account for this. Using 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 changed as appropriate depending on how the coordinate system of FIG. 5 is defined.

[0027]

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[0028]

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[0029] B. As shown in Figure 6, the direction of the eye axis from the center of eye rotation toward the intersection point, i.e., 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 coordinates of the node are transformed from N to N' according to Listing's law, which is based on the light ray emitted from the back surface of the lens when the eye axis points toward the intersection point. With the lenses to be designed or evaluated worn in both eyes, assuming a light ray emitted from the intersection point (Pr, Pl) whose coordinates were calculated in A toward eye rotation, the amount of eye rotation is obtained as a rotation matrix L from the first eye position vector G1 in straight-on gaze and the third eye position vector G3 based on the light ray emitted from the back surface of the lens. Here, θi is calculated again using Equation 3 above, and an arbitrary coordinate P in three-dimensional space with the eye rotation as the origin is transformed into coordinate P' after rotation in the third eye position direction. That is, it is the formula of the following formula 7. The rotation matrix L is the Rodrigues rotation matrix L of the above formula 4.

[0030]

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[0031] The initial fovea (Fr, Fl) is coordinate-transformed using the rotation matrix L obtained in CB. 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, straight ahead 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 wearer's standard axial length, the point F0 is defined as (16.5 + Δ,0,0) accordingly. b) As shown in Figure 2, coordinate transformation is performed on F0 by the temporal deviation angle α and the downward deviation angle β to find the initial foveal position F. The initial foveal position F corresponds to the third intersection point. This calculation is performed using the following formula 8. A coordinate transformation (rotation matrix Y(α)) that rotates the Y axis taking into account the deviation angle α rotates F0 toward the ear, and then a coordinate transformation (rotation matrix Z(β)) that rotates the Z axis taking into account the deviation angle β rotates F0 toward the lower retina. This is because the fovea is shifted by α toward the ear and β downward with respect to the eye axis, using the nodal point as the reference 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.

[0032]

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[0033] c) As shown in FIG. 7, the initial foveal position F(Fr, Fl) in b) above is coordinate-transformed into the specified third eye position direction using rotation matrix L to determine 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. The rotation matrix L is the Rodrigues rotation matrix L in formula 4 above. At this time, in order to change the origin from the nodal point to the eye's center of rotation, the distance from the nodal point to the eye's center of rotation (fixed at 5.6 mm in this embodiment) is subtracted from the x-coordinate of the foveal position F before coordinate transformation.

[0034]

number

[0035] The position of the fovea (Fr', Fl') when the gaze of each eye is directed toward the fixation point T is obtained by DC, so with the lenses to be designed or evaluated worn in each eye, the chief ray traveling from the fixation point T to the fovea (Fr', Fl') is considered, and the lens power (S, C, AX, Prism / Base, etc.) for each eye at various points when looking at the fixation point T is calculated. More specifically, a) The chief ray passes through the lens from the gaze point T and reaches the fovea (Fr', Fl'). The angle of incidence of the chief ray (the angle of incidence from the gaze point to the lens surface) is calculated. At this time, the angle of incidence is adjusted taking into account the refraction at the front and back surfaces of the lens so that it reaches the fovea. b) Secondary rays are set at 2-degree intervals at positions 1.5 mm radius (i.e., pupil diameter) away from the gaze point of the principal ray, and are transmitted through the lens in the same way as the principal ray at the incident angle of a) above. c) Calculate the distance (focal length f: unit mm) to the point where the chief ray and at least two secondary rays reach the rear surface of the lens and come closest to each other to find the lens power. The maximum lens power is the S power, and the minimum lens power is the S+C power. Here, in this embodiment, since the transmitted light wearing power must be calculated when there is a bend angle and an anterior tilt angle, the position of the fixation point T must be changed according to the bend angle and anterior tilt angle, and the calculation must be performed taking into account the chief ray heading from the changed fixation point T to the fovea (Fr', Fl'). Therefore, the calculation is performed as follows.

[0036] First, we will explain how the difference occurs when there is a warp angle or forward tilt angle when the lens is attached to the eyeglass frame compared to when there is no warp angle or forward tilt angle. FIG. 9 is a schematic diagram showing how the line of sight changes and how the point of gaze changes accordingly when the angle of curvature (or forward tilt angle) is φ, as an example when looking straight ahead. Let the intersection of the eye axis and the retina be (0, 0), and assume that the fovea is located at said intersection. Then, consider a gaze vector that starts from said intersection and points directly ahead toward the gaze point P0. At this time, the gaze vector is affected by refraction when passing through the lens and by the lens tilt due to the bending angle (or forward tilt angle) φ, so it shifts from the original gaze point P0 to the gaze point P at a certain angle θ. This can be expressed as follows:

[0037]

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[0038] Here, Trans(θ) indicates coordinate transformation of point P0 to point P based on angle θ, and can be expressed by the following rotation matrix, for example. Therefore, it shifts to the gaze point P. This can be simply expressed as the following equation:

[0039]

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[0040] The above-mentioned "certain angle θ" can be determined by, for example, considering an incident vector Q0(X,Y,Z) = (1,0,0) that is incident straight onto the lens from the starting point, and calculating the vector Q(X,Y,Z) after passing through the lens surface obtained by ray tracing calculations that take into account the tilt of the lens, and then determining the angle formed by the two vectors mentioned above. Taking into account how the gaze point shifts when there is a curvature angle or forward tilt angle, we consider calculating the coordinates of the modified gaze point P, assuming that there is a deviation angle (α, β) of the visual axis relative to the eye axis. According to the deviation angle (α, β) of the visual axis relative to the eye axis, the original gaze point P0 is calculated, as shown in Figure 9, taking into consideration how far the fovea is from the eye axis. The original gaze point P0 corresponds to T0' in the above-mentioned formula (5). Next, consider an incident vector starting from the fovea, which is positioned off the eye axis, and heading towards the above-mentioned P0 (=T0'), find the angle of deviation from P0 (the above-mentioned "certain angle θ"), and use coordinate transformation according to θ to find fixation point P', which is positioned off by "certain angle θ" from P0. Fixation point P' is the "changed fixation point T" in the above explanation, so a) to c) in paragraph 0033 are carried out for this fixation point P.

[0041] (3) Specific calculations The above 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 formula in equation 12 below. In the formulas below, the back side is represented as Ura and the front side as Omote. Because there is C power, the curve direction is set to two perpendicular directions. In the vector calculations below, the X-axis direction is constant, and only the Y-axis and Z-axis directions change.

[0042]

number

[0043] Next, the chief ray that passes through the fovea after passing through the lens when the visual axis is directed in a certain direction is calculated. Here, the refracted vector of the light ray after passing through the surface of the lens is calculated by the vector function formula in the following formula 13, and the refracted vector of the light ray after passing through the back surface of the lens is calculated by the vector function formula in the following formula 14. In this formula, the incident vector of the chief ray on the lens surface is adjusted so that it passes through the fovea after passing through the lens.

[0044]

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[0045]

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[0046] Now, let's 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 point through which the ray passes and the sag at a point that is slightly changed (ΔY, ΔZ) from the pass point. The vector elements Ey and Ez can be expressed as shown in Equation 15 and Equation 16. The formula for calculating the sag at the lens surface in Equation 15, which refers to the vector Q0mote after refraction after passing through the front surface, is expressed by Equation 17. Furthermore, the formula for calculating the sag at the lens back surface in Equation 16, which refers to the vector Qura after refraction after passing through the back surface, is expressed by Equation 18. Equations 17 and 18 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.

[0047]

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[0048]

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[0049]

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[0050]

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[0051] As described above, the sag value of the lens with the fovea as the reference point is determined for the design lens. A specific eyeglass lens is manufactured based on this sag value. The eyeglass lens with this design is then manufactured as an asymmetric lens, even if it is a single-vision lens without astigmatism power. The reason why a single-vision eyeglass lens designed with the fovea as the reference point is asymmetric will be explained below. Equation 19 is an equation that shows the relationship between a point on the back surface of a lens and the focal length at that point. Equation 19 is used when performing ray tracing simulations for the chief ray and secondary rays based on the post-refraction vector Qura after passing through the back surface and the point passing through the back surface. This is because secondary rays around the chief ray are required to calculate the focal length. Specifically, this simulation is performed, for example, as follows: i) As shown in Figure 8, multiple starting points of secondary rays are placed at intervals of angle θ on a circle 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 subsequent power calculations easier. ii) For a secondary ray in a certain θ direction and a secondary ray 180 degrees opposite to it, the point at which it passes through the back surface of the lens and its vector after refraction at the back surface of the lens are found by ray tracing, and the point at which the chief ray passes through the back surface of the lens and its vector after refraction at the back surface of the lens are also used to calculate the focal length and obtain the power according to equation 19 below. Because ray tracing is performed in three-dimensional space, the chief ray is also considered in addition to the two secondary rays to prevent the rays from twisting and reducing the accuracy of the focal length calculation.

[0052]

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[0053] iii) Execute step ii) above for each angle θ to find the power for each angle θ. Then, set the maximum power as the S power, the minimum power as the S+C power, and set the angle at which the power is maximum as the astigmatic axis.

[0054] Again, the coefficient α in equation 19 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 at a distance from the chief ray that is the radius of the pupil diameter, so in the simulation of this embodiment, the beam diameter is the distance from a point on the lens surface to be evaluated to a position (the position of the secondary rays) that is the radius of the pupil. Therefore, the beam diameter_ur and the beam diameter_K are calculated as the distance between the chief ray and a pair of adjacent secondary rays. Point K (the eye's center of rotation) is used as the beam diameter because its position does not change even when the eye moves, which is advantageous for calculations. If the lens has a negative power, α will be a negative value because luminous flux diameter_ur<luminous flux diameter_K, and if the lens has a positive power, α will be a positive value because luminous flux diameter_ur>luminous flux diameter_K. Also, the greater the difference between luminous flux diameter_ur and luminous flux diameter_K, the greater the absolute value of the lens power that is obtained.

[0055] The beam diameter K associated with the coefficient α depends on the refraction vector (tanY_ura, tanZ_ura) in equation 19 after the chief ray passes 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 diverges after passing through the lens, 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.

[0056] Next, a simulation of a lens designed according to the method of the present invention under the following conditions will be performed, and an example of calculation of the foveal position when the lens is tilted due to the bending angle or forward tilt angle will be shown. The deviation angles (α, β) of the visual axis relative to the eye axis were set to α = 5.5 (degrees) and β = 0.0 (degrees). The standard axial length was set to 24 mm. In this case, the distance from the apex of the lens back surface to the apex of the retina was 36 mm (the distance changes if the axial length changes). S degree S-5.00 Warp angle 20 degrees Forward tilt angle 8 degrees Distance between vertices: 12mm Center thickness CT=1.1(mm) Substrate refractive index n = 1.600 Table curve 4.00 curve (substrate refractive index equivalent) Surface curvature radius r0 = 1000·(n-1) / 4.00 = 150 (mm) Surface curvature Co=1 / r0=0.00666(mm -1 ) Principal curvature of the inner surface Cx=(4.00-(-4.00)) / (1000·(n-1))=0.01333(mm -1 ) Cy=(4.00-(-4.00)) / (1000·(n-1))=0.01333(mm -1 )

[0057] Since the actual calculation is complicated, it will be explained here in a simple and simplified manner. Here, the calculation of the camber angle will be explained as an example, but the calculation of the forward lean angle can also be performed in the same way as the calculation of the camber angle. First, as shown in Figure 9, starting from the starting point (0, 0) on the retina, the incident vector Q0(X, Y, Z) = (1, 0, 0) and the vector Q(X, Y, Z) after passing through the lens surface is calculated as Q = (1, 0, -0.19). By calculating the dot product of these two vectors, the deviation angle θ of the gaze point due to the bend angle when looking straight ahead is calculated to be θ = 0.19 (rad). Next, when α = 5.5 (degrees) and β = 0.0 (degrees), and looking straight ahead, the coordinate F of the fovea relative to the eye axis is calculated as F(x, y, z) = (35.91, 0, -0.76) (units: mm). Here, the aforementioned x-coordinate is a value when the vertex of the rear surface of the lens is the origin. Also, the fixation point corresponding to the calculated position coordinate F of the fovea is the fixation point before the bend angle is applied. Here, since the angle of deviation of the gaze point is roughly the same (i.e., θ = θ'), the calculated position coordinate F of the fovea can be transformed using a rotation matrix based on the θ (= 0.19) calculated above, and the position coordinate F' (x, y, z) = (35.48, 0, 5.97) of the fovea relative to the gaze point that has changed (shifted) due to the influence of the deflection angle can be calculated according to the following equation. Here, in the coordinate transformation of the above equation, the direction of rotation is opposite to the direction in which the gaze point shifts, so θ in the coordinate transformation function becomes negative.

[0058]

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[0059] Figure 10 shows the results of a simulation of the calculated spherical equivalent power (S power + C power / 2) when the line of sight is moved from the center of the lens onto the horizontal axis, assuming an aspheric lens with the above-mentioned curvature angle and prescription power. This is compared with the results of a simulation in which the deviation angle between the ocular axis and the visual axis is not taken into account, and also with the results of a simulation in which the deviation angle between the optical axis and the visual axis corresponding to each axial length is taken into account (three axial lengths: 20 mm, 24 mm, and 28 mm). In addition, the tracking coordinates on the horizontal axis shown on the vertical axis indicate the ear side in the plus direction and the nose side in the minus direction. As can be seen in Figure 10, when looking at the center of the lens, the power changes depending on whether or not the fovea is taken into account in the simulation, and the change in power is even greater when looking at the periphery of the lens. Also, although the fovea is taken into account in the simulation, comparing the deviation angles between the optical axis and the visual axis for axial lengths of 20 mm, 24 mm, and 28 mm shows that there is a difference in power when looking at the center of the lens, but this is even more pronounced at the periphery of the lens (especially at a position about 15 mm away from the center toward the ear), indicating that correction according to the axial length is necessary.

[0060] Furthermore, for an aspheric lens with the power distribution shown in Figure 10, the equivalent spherical power at the center of the lens, the point 16 mm to the ear, and the point 16 mm to the nose, as well as the difference in equivalent spherical power at each of the aforementioned points on the ear and nose sides relative to the center of the lens, when the fovea is not considered and when the fovea is considered, and when the axial length is different when the fovea is considered, the results are summarized as shown in the table in Figure 11. Figure 12 is a table showing the relationship between the power difference ΔD at specified points on the nose and ear sides and the correction rate of the target power. The power difference ΔD at specified points on the nose and ear sides based on Figure 11 was simulated, and the resulting correction rate follows the table in Figure 12. According to the table in Figure 11, when the fovea is not taken into consideration, the difference in power at the specified points on the nasal and temporal sides of the lens center is approximately ±0.70 D, so the correction rate of the target power is small (approximately 50% in the table in Figure 12). On the other hand, when the fovea is taken into consideration, the aforementioned power difference falls within approximately ±0.4 to 0.5 D in all cases, and the correction rate of the target power is relatively large (approximately 90% in the table in Figure 12). Furthermore, although it is not necessary to change the correction rate depending on the axial length, because the transmitted light wearing power before correction differs depending on the axial length, it can be seen that the final corrected wearing power will differ even if an automatically adjusted correction rate of 90% is applied in the same way.

[0061] With the above configuration, the embodiment provides the following effects. (1) The position of the fovea (Fr', Fl'), whose coordinates are unknown, can be found based on the intersection point (Pr, Pl) or nodal point, the center of rotation, and the deviation angle, which are clear coordinates that pass through the eye axis. This makes it possible to trace rays using a visual axis based on the fovea (Fr', Fl'), allowing for more accurate verification of the user's visual condition. Furthermore, by using such a fovea (Fr', Fl') as the reference, the position of the gaze point can be changed taking into account the curvature angle, and the transmitted light wearing power can be obtained through a simulation based on a new gaze point. (2) By performing coordinate transformation using a rotation matrix before calculating the fovea (Fr', Fl'), accurate and optimal calculations for the rotating eyeball model are possible. (3) By simulating differences in axial length as a parameter, the transmitted light power can be obtained, enabling fine-tuned power settings to suit the individual wearer's eyes.

[0062] 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 also be embodied in modified forms, for example, as follows. The above embodiment is an example. The calculation may be performed in an order other than the above. In the above embodiment, the case where both a bending angle and a forward tilt angle are present has been described, but the present invention may be applied to an eyeglass frame having only one of these angles. In the specific calculations above, the sag value is calculated taking aspheric sag into account in equations 17 and 18, but it is also possible to calculate the sag value using only the basic sag value and then calculate the aspheric sag separately later and add it all together. Similarly, in the case of a progressive power lens, it is necessary to consider the progressive sag, but as with the aspheric sag, it is also possible to calculate the progressive sag in equations 17 and 18 from the beginning, or to calculate it separately later and add it all together. The above number and positions of secondary rays in the simulation are just examples, and calculations may be performed using numbers and positions of secondary rays other than those described above. The above example was a simulation using a single-vision lens, but it is also possible to simulate the case where progressive power lenses are worn in an eyeglass frame with a curvature angle, etc. In the above embodiment, a calculation method assuming a frontal view was given as an example for determining the intersection point (Pr, Pl), but it may also be determined by calculation from a direction other than a frontal view, with the specified gaze point T as the base. The lenses to be designed or evaluated in the simulation can be any type used as spectacle lenses, such as spherical lenses, aspherical lenses, and progressive power lenses. In the above example, the values ​​measured at the eyeglass retailer are accessed via the internet to the manufacturer's website, but this is just one example; input data can also be provided without going via the internet and calculated on the manufacturer's computer. [Explanation of symbols]

[0063] 15...Server as a computer device.

Claims

1. A method for calculating the correction power of a spectacle lens by computer simulation, in which a lens with a predetermined prescription power is fitted into an eyeglass frame with a curvature angle, and the transmitted light wearing power obtained when the eyeglass frame is worn in a state with the curvature angle is corrected so as to approach the predetermined prescription power, a computer device is used to perform a simulation in which a light ray is transmitted through an eyeball model and a lens arranged in front of the eyeball model, and the light ray reaches a gaze point; data on the eyeball model's eye axis is obtained; and position data of the fovea in the eyeball model is calculated using the data on the eye axis; A method for calculating the correction power of eyeglass lenses, characterized by changing the position of the gaze point according to the bend angle, performing a simulation to obtain a ray of light passing through the visual axis connecting the position data of the fovea and the nodal point based on the new gaze point, calculating the transmitted light wearing power based on the obtained ray of light, and calculating the correction power based on the transmitted light wearing power.

2. A method for calculating the correction power of a spectacle lens by computer simulation, in which a lens with a predetermined prescription power is fitted into a spectacle frame with a forward tilt angle, and the transmitted light wearing power obtained when the lens is worn in a state with the forward tilt angle is corrected so as to approach the predetermined prescription power, a computer device is used to perform a simulation in which a light ray is transmitted through an eyeball model and a lens arranged in front of the eyeball model, and the light ray reaches a gaze point; data on the eyeball model's eye axis is obtained; and position data of the fovea in the eyeball model is calculated using the data on the eye axis; A method for calculating the correction power of eyeglass lenses, characterized by changing the position of the gaze point according to the forward tilt angle, performing a simulation to obtain a ray of light passing through the visual axis connecting the position data of the fovea and the nodal point based on the new gaze point, calculating the transmitted light wearing power based on the obtained ray of light, and calculating the correction power based on the transmitted light wearing power.

3. 3. The method for calculating the correction power of a spectacle lens according to claim 1, wherein the coordinates of the fixation point are converted by a rotation matrix to be changed to the new fixation point.

4. 3. The method for calculating the correction power of eyeglass lenses according to claim 1, wherein the calculation for performing a simulation to obtain light rays passing through the visual axis is performed using different parameters depending on the axial length.

5. 3. The method for calculating the correction power of eyeglass lenses according to claim 1, further comprising: calculating a differential power, which is the difference between the predetermined prescription power and the transmitted light wearing power calculated based on a new gaze point; and calculating the correction power based on the difference between the target power and the differential power.

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