JP2003052633A - Simulation instrument of ophthalmological optical system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a simulation instrument of an ophthalmological optical system, which is capable of simulating a shake, a distortion, a blurring or the like in a case where a lens system of a varifocal lens is worn. SOLUTION: A torsional retinal image defined as an image in which images captured in the central fovea by rolling the eyeballs to all object points within a visual field are united together is prepared by preparing an image of a specific angle of a visual field entering the eyes having a specific center of torsion as an original image, making a distorted original image involving a distortion when the original image is seen through a lens system by a ray tracing method, obtaining a PSF on the retina of an eyeball model due to light from the object points of the original image in an optical system made up of a lens system and an eyeglass model, and computing the convolution of the distorted original image obtained and the PSF of every picture element of the original image. The torsional retinal image obtained is edited to obtain a moving image of the torsional retinal image. The PSF is obtained by setting sample points at object points and the PSF other than sample points is obtained by an approximation method including a spline interpolation method.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an ophthalmic optical system simulating apparatus for simulating the appearance of an external world through a lens system arranged in front of the eye.

[0002]

2. Description of the Prior Art Disclosed is a method and apparatus for simulating an eye optical system for simulating the appearance when observing the outside world through a lens system arranged in front of the eyes such as when wearing spectacles. There is an apparatus described in Japanese Patent Application Laid-Open No. 8-266473 related to the applicant's earlier application.

The apparatus described in the above publication simulates a scene image in a range that can be overlooked by the rotation of the human eye while wearing a spectacle lens by performing PSF calculation or the like. This makes it possible to simulate a wide-angle scene accompanied by rotation of the human eye when wearing an optical lens such as spectacles.

[0004]

By the way, in particular, when a progressive power multifocal lens is worn, the user may feel uncomfortable feeling such as shaking, distortion, blurring or the like, instead of fulfilling the bifocal function. Therefore, when designing a progressive multifocal lens,
It is required to reduce discomfort as much as possible while realizing the bidirectional function. For this purpose, it is most desirable for the designer to know in advance how the designed lens is accompanied by discomfort such as shaking, distortion, and blurring.
The above-described conventional method for simulating an eye optical system is very useful for a certain purpose because it can simulate a wide-angle scene accompanied by rotation of the human eye when wearing an optical lens such as spectacles. However, the simulation was not performed in a manner close to the actual one in consideration of distortions, blurring and the like that the wearer might feel, even taking into account human perceptual effects. Therefore, when the wearer wears the designed lens, it is not always sufficient for the purpose of letting the designer know in advance what kind of distortion, blurring, etc. the wearer actually feels. It wasn't something. Moreover, it was not possible to deal with the shaking that seems to be the most problematic when actually worn.

It is considered that the external image perceived (perceived) by the human through the eye is not the optical image itself formed on the retina of the eye according to the optical principle. That is, the distribution of photoreceptors (cones and rods) on the retina is high in the vicinity of the fovea and low in the periphery. Therefore, if the optical image itself formed on the retina is perceived, even if the optical image is ideally formed, only the center is clear and the periphery is blurred. Should be perceived as. However,
If you have normal eyes, you can see clearly anywhere in the visual field. It is thought that this is because the action of perception is not based on the simple action of directly detecting the optical image projected on the retina, but on the result of complicated processing by the neural information processing system after the retina. Because it will be done.

According to the research conducted by the present inventors, such a perceptual action cannot be directly simulated, but based on certain assumptions found by the present inventors, the result of the perceptual action can be approximated by image processing. It was clarified that it can be reproduced visually.

The present invention has been made under the above-mentioned background, and it is possible to simulate the visual appearance accompanied by shaking, distortion, blurring and the like when a lens system such as a progressive multifocal lens is worn. The purpose is to provide an academic simulation device.

[0008]

According to a first aspect of the present invention, there is provided an eye-optical system simulation apparatus for simulating the appearance when the external world is observed through a lens system arranged in front of the eye. As the perceived image, not the optical image projected on the retina surface of the eye, but the rotation defined as the image in which the eyeball is rotated with respect to all object points in the visual field and the images captured in the fovea are joined. It is characterized by further comprising a rotating retinal image creating means for creating a retinal image.

According to a second aspect of the present invention, in an eye optical system simulating apparatus for simulating the appearance when the outside world is observed through a lens system arranged in front of the eye, an image perceived by the eye through the lens system is: Rotation that creates a convoluted retina image that is defined as the image obtained by combining the images captured in the fovea with the eyeball for all object points in the visual field, rather than the optical image projected on the retina surface of the eye. The retinal image creating means includes an original image creating means for creating as an original image an image having a specific viewing angle that enters an eye having a specific center of rotation, and the original image is viewed through a lens system. Distortion source image creating means for creating a distortion original image with a ray tracing method, and an optical system consisting of a lens system and a spectacle model, which uses light from an object point of the original image. A convolution operation is performed between the PSF acquisition unit that obtains the PSF on the retina of the eyeball model, the original distortion image obtained by the original distortion image creation unit, and the PSF of each pixel of the original image obtained by the PSF acquisition unit. And a convolution operation means.

A third aspect of the present invention is a simulation apparatus of an eye optical system for simulating the appearance when the outside world is observed through a lens system arranged in front of the eye, wherein a virtual object based on computer graphics in a virtual three-dimensional space. This virtual object creates an image of a specific viewing angle that enters the eye having a rotation center point at a specific position and has a specific central line-of-sight direction as an original image, and Original image creating means for obtaining the object point distance which is the distance between the object point position represented by the pixel and the center of rotation of the eye, and the central line-of-sight passing point is set on the lens system arranged in front of the eye, and the visual field A ray which is emitted from a central object point, passes through the central line-of-sight passage point, and is directed toward the rotation center point is obtained by a ray tracing method, and the obtained ray direction of the lens system is used as the central line of sight. Is defined as the field of view after passing through the lens system, the direction of the line of sight to the corresponding object point of each pixel of the original image in this field of view after passing through the lens system and the lens system passing point are determined by the ray tracing method, and A distortion original image creating means for creating an image including distortion, and an accommodation eyeball model as an optical system of the eye are introduced, and for each pixel of the original image, the object point distance obtained by the original image creating means. And, the adjustment state of the eyeball model is set according to the power at the lens system passing point of the chief ray emitted from the object point obtained by the distortion original image creating means, according to the lens system and its chief ray direction. In a synthetic optical system with a convoluted eyeball model, a PSF (Point Spread Function) representing the luminance distribution on the retina of the accommodation eyeball model corresponding to the light emitted from the object point PSF obtaining means for obtaining the PSF, an image including distortion caused by the lens system created by the distortion original image creating means, and the PS
Convolution with the PSF of each pixel obtained by the F acquisition means was performed, and the virtual object placed in the virtual three-dimensional space was viewed through a specific position of the lens system with a specific position and an eye in the line-of-sight direction. And convolution means for creating a convoluted retinal image in the case.

According to a fourth aspect of the present invention, in a simulation apparatus of an eye optical system for simulating the appearance when the external world is observed through a lens system arranged in front of the eye, a virtual object based on computer graphics in a virtual three-dimensional space. Is created and arranged, and a story is created by viewing the eye position, the central line-of-sight direction, and the lens system passing point in time series, and the second or third story is created at each time point according to the story.
The invention is characterized in that a rotating retinal image is created using the eye optical system simulation apparatus according to the invention, and each retinal image is edited to create a moving image of the rotating retinal image.

In a fifth aspect of the present invention, in the eye optical system simulation apparatus according to any one of the second to fourth aspects, the PSF acquisition means emits light from an object point represented by each corresponding pixel, and the eyeball model. All data of rays passing through each point set by equally dividing the entrance pupil of is obtained by the ray tracing method, and PSF is obtained as a ray spot distribution density on the retina of the eyeball model or as a diffraction integral based on wave optics. It is characterized by

According to a sixth aspect of the present invention, in the eye optical system simulation apparatus according to any of the second to fourth aspects, the PSF acquisition means sets a finite number of object sample points in advance in the three-dimensional object space. , A finite number of passing sample points on the entrance pupil plane are selected, ray data by all combinations of the object sampling points and passing point sampling points are obtained by a ray tracing method, and spline interpolation coefficient data is created, Ray data emitted from an object point represented by each pixel of the original image and passing through each point obtained by equally dividing the entrance pupil is obtained by a spline interpolation method using the spline interpolation coefficient data prepared in advance, and a PSF on the retina is obtained. It is characterized in that it is obtained as the spot distribution density of light rays or as a diffraction integration method based on wave optics.

In a seventh aspect of the present invention, in the ophthalmic optical system simulation apparatus according to any of the second to fourth aspects, the PSF acquisition means approximates the PSF by a certain function and expresses it by its parameter, and the PSF is cubic in advance. Select a finite number of object sampling points in the original object space, and select PS for all object sampling points.
F and its approximate function parameters are obtained, spline interpolation coefficient data is created, and PSF for each pixel of the original image is obtained.
The parameter is obtained by a spline interpolation method using the previously prepared spline interpolation coefficient data.

According to an eighth aspect of the present invention, in the simulation apparatus for an eye optical system according to any of the second to seventh aspects, the convoluted retinal image or the moving image of the convoluted retinal image is displayed by image display means, and It is characterized in that the image display means displays which position of the lens system the image is through.

A ninth aspect of the present invention is a simulation apparatus of an eye optical system for simulating how an external world is observed through a lens system arranged in front of an eye, wherein a virtual object created by computer graphics in a virtual three-dimensional space. This virtual object creates an image of a specific viewing angle that enters the eye having a rotation center point at a specific position and has a specific central line-of-sight direction as an original image, and Original image creating means for obtaining the object point distance which is the distance between the object point position represented by the pixel and the center of rotation of the eye, and the central line-of-sight passing point is set on the lens system arranged in front of the eye, and the visual field A ray which is emitted from a central object point, passes through the central line-of-sight passage point, and is directed toward the rotation center point is obtained by a ray tracing method, and the obtained ray direction of the lens system is used as the central line of sight. Is defined as the field of view after passing the lens system, the direction of the line of sight to the corresponding object point of each pixel of the original image in the field of view after passing the lens system and the medical lens system passing point are obtained by the ray tracing method, and the lens system Distortion original image creating means for creating an image including distortion, and by introducing an accommodation eyeball model as the optical system of the eye, for each pixel of the original image, the object point obtained in the original image creating step Set the adjustment state of the eyeball model in accordance with the distance and the power at the lens system passing point of the chief ray emitted from the object point obtained in the distortion original image creating step, according to the lens system and its line-of-sight direction. In a synthetic optical system with a rotated eyeball model, a PSF acquisition unit for obtaining a PSF representing a luminance distribution on the retina of the accommodation eyeball model corresponding to the light emitted from the object point, and the original distortion image. A convolution operation is performed between the image including distortion caused by the lens system created in the forming step and the PSF of each pixel obtained in the PSF acquisition step, and the virtual object placed in the virtual three-dimensional space is placed at a specific position and line-of-sight direction. And a convolution means for creating a convoluted retinal image when viewed through a specific position of the lens system.

A tenth aspect of the present invention is a simulation apparatus for an eye optical system for simulating the appearance when the external world is observed through a lens system arranged in front of the eye,
Create a virtual object by computer graphics in a virtual three-dimensional space and arrange it, create a story by changing the eye position, central line of sight direction and lens system passing point in time series, and create a story according to that story A ninth aspect of the present invention is characterized by having means for creating a revolved retinal image, editing each retinal image, and creating a moving image of the revolved retinal image.

An eleventh aspect of the invention is an apparatus for simulating an eye optical system according to the ninth or tenth aspect of the invention, which displays the convoluted retina image or a moving image of the convoluted retina image, and these images are displayed in the lens system. It is characterized by having an image display means for displaying through which position of the image.

[0019]

DESCRIPTION OF THE PREFERRED EMBODIMENTS (Embodiment 1) FIG. 1 is a diagram showing a flow of creating a retina image of rotation in a simulation method of an eye optical system according to a first embodiment of the present invention, and FIG. FIG. 3, FIG. 3 is a diagram showing a coordinate system of a convoluted retinal image when a lens system is worn, FIG. 4 is a diagram showing optical parameters (non-adjusted state) of a Navarro model eye, and FIG. 5 is a crystalline lens of a Navarro model eye. 8 is a diagram showing the adjusting force dependence formula of FIG. 6, FIG. 6 is an explanatory diagram of PSF, FIG. 7 is a diagram showing the relationship between ray tracing and the entrance pupil, and FIG.
Is a diagram showing a method of dividing an entrance pupil, and FIG. 9 is a diagram showing a retina position and an incident angle. Hereinafter, a simulation method of an eye optical system according to Example 1 of the present invention will be described with reference to these drawings.

The simulation method of the eye optical system according to this embodiment is a method of obtaining a still image of a revolving retinal image when a three-dimensional object image created by computer graphics is viewed through a lens. The convoluted retinal image is based on a certain assumption found by the inventors of the present invention, and by subjecting the three-dimensional object image to image processing in consideration of an optical effect, an image perceived by the eye can be approximated. It is a reproduced image. In other words, the convoluted retinal image is not an optical image projected on the retina surface of the eye, but is defined as an image in which the images captured by the fovea are combined by rotating the eyeball with respect to all object points in the visual field. It

The ophthalmic optical system simulation method according to the first embodiment is roughly divided into (1) original image creating step, (2) distortion original image creating step, (3) PSF acquisition step, (4) convolution step, Consists of.

(1) Original image creating step In this step, a virtual object by computer graphics is created and arranged in a virtual three-dimensional space, and this virtual object places a rotation center point at a specific position and a specific point. A step of creating an image of a specific viewing angle that enters the eye having a central line-of-sight direction as an original image, and obtaining an object point distance that is a distance between an object point position represented by each pixel of the original image and a rotation center point of the eye Is. This will be described below.

Creation of Virtual Object Image as Base of Original Image First, a virtual three-dimensional object is created and arranged in a virtual three-dimensional space by a well-known computer graphics technique. For example, an image is created by arranging a desk, chair, furniture, etc. in the room, or arranging flower beds, trees, signs, etc. outdoors.

Creation of Original Image An image with a specific viewing angle is created as an original image in which the virtual object created above enters the eye having a rotation center point at a specific position and a specific central line-of-sight direction. That is, as shown in FIG. 2, the field quadrangular pyramid A ₁ A ₂ A ₃ A ₄ is set as the specific field of view. The center A of the visual field quadrangular pyramid A ₁ A ₂ A ₃ A _{4 is} the center of the visual field. The line connecting A and the center of rotation O is the central line of sight, which is the x-axis, and O is the origin. Then, the rotational retinal coordinates of an arbitrary point P (x, y, z), which is an arbitrary object point in the quadrangular pyramid, is Ψ = tan β = y / x, ζ = tan γ = z / x
And Here, β and γ are azimuth angles of P (x, y, z). If each object point in the visual field is represented by this coordinate system, an arbitrary straight line in space appears as a straight line on the convoluted retinal image. The image representing each object point in this coordinate system is the original image. Also, P (x,
Each object point distance is obtained from the coordinate values of (y, z).

(2) Distortion Original Image Creating Step In this step, the central sight line passing point is set on the lens system arranged in front of the eye, and the light is emitted from the visual field center object point and passes through the central sight line passing point. , The ray toward the center of rotation is obtained by the ray tracing method, and when the field of view with the obtained ray direction of the lens system as the central line of sight is defined as the field of view after passing through the lens system, the original image in the field of view after passing through this lens system is defined. In this step, the direction of the line of sight to the corresponding object point of each pixel and the lens system passing point are obtained by the ray tracing method, and an image including distortion due to the lens system is created.

That is, as shown in FIG. 3, the lens L is arranged at a position close to O in the middle of the origins O and A in FIG. The light ray emitted from the object point within the quadrangular pyramid is refracted by the lens L and reaches the point O. Therefore,
In order to gaze at point A, the eyeball must be oriented in the OB direction. The quadrangular pyramid representing the visual field also becomes B ₁ B ₂ B ₃ B ₄ (visual field after passing through the lens system). The rotating retina image at that time is x '
A coordinate system in which the axis is the gaze line (center line of sight) must be taken. This is obtained by ray tracing in consideration of the power of each point on the lens, and the image based on the thus obtained object point coordinates is used as a distorted original image.

As described above, when the lens passes through the lens, the relative positional relationship of each point in the visual field changes, unlike the case of the naked eye. This is the cause of distortion of the spectacle lens. The OB direction changes depending on the lens use position. Especially in the case of a progressive lens, the change is drastic. Other light rays in the field of view also change the angle of incidence on the eye, and in particular in the case of a progressive lens, the change is uneven, so that they are perceived as shaking or distortion.

(3) PSF acquisition step In this step, an accommodation eyeball model is introduced as an optical system of the eye, and for each pixel of the original image, the object point distance obtained in the original image creation step and the distorted original image The adjustment state of the eyeball model is set according to the power of the principal ray emitted from the object point obtained in the creation process at the lens system passing point, and the synthetic optics of the lens system and the eyeball model rotated according to the direction of the principal ray. In the system, the PSF (Point Spread F
unction: Point spread function).

Introduction of accommodation eye model for accommodation Since the image of the original strain image formed on the retina through the optical system of the eye is a convoluted retinal image, it is necessary to introduce a model of the optical system of the eye. In this case, the eye has an adjusting effect according to the object distance, which must be taken into consideration. In this example, R.Nav, which is an eyeball model that also considers the accommodation effect, is used.
The accommodation-dependent eye model by Arro et al. was used. Navarro
In the model, not only the paraxial value but also the spherical aberration and the chromatic aberration are adapted to the actually measured value of the eye. It has a simple four-sided structure, three of which are quadratic aspherical surfaces. The crystalline lens does not have a refractive index distribution structure and tracking calculation is easy. The radius of curvature, the thickness, and the asphericity change in proportion to the logarithm of the adjusting power. FIG. 4 shows the optical parameters of the Navarro's accommodation-dependent eye model in the absence of accommodation. Further, FIG. 5 shows a dependence formula of the parameter depending on the adjustment. Aspherical surface is y
Represented by ^{2 + z 2 + (1 +} Q) x 2 -2Rx = 0. Q is the asphericity.

Calculation of PSF a. Meaning of PSF In general, the optical image of the optical system is obtained by obtaining the PSF of the optical system and performing convolution calculation with the real image. As shown in Fig. 6, this PSF is a point where the light rays emitted from one point of the real object are focused on the image plane.
It is a function that represents the aggregated state of (spots), and can be represented by the number of spots per unit area. In the case of a perfect optical system, the PSF has all spots gathered at the image formation point and its distribution is a vertical straight line, but it usually has a shape similar to a spread Gaussian distribution. Since the object is considered to be composed of points, the image can be obtained by convolution of the brightness distribution of the object and PSF.

B. PSF calculation method Figure 7 shows the object point P when viewed through point Q on the lens.
It is a figure which shows the relationship between a tracking ray and an entrance pupil in the optical system for calculating | requiring PSF. The light ray from the object point P is refracted at the lens surface point Q, the emission direction changes, and reaches the turning point O. To the eyes, the object point P seems to be on the extension line of the outgoing ray direction QO. Thus, when viewing P, the optical axis of the eyeball is first rotated in the QO direction, and then the distance of P and Q
Adjust the degree of adjustment according to the refractive power of the point. At this point, the optical system is solidified and the PSF can be obtained.

As described above, the PSF is the density of the spot on the image plane of the light rays emitted from the object point and passing through the centers of a large number of areas into which the entrance pupil is evenly divided. Strictly speaking, the position of the entrance pupil is the object-side conjugate point of the pupil. However, the position of the pupil changes due to rotation, and the position of its conjugate point also differs depending on the adjustment state. On the other hand, the position of the center of rotation is fixed, and the distance from the conjugate point of the pupil is smaller than the object distance. Therefore, in the case of the naked eye, the position of the entrance pupil can be considered as the center of rotation. When wearing glasses,
The entrance pupil of the entire optical system is a conjugate point of the center of rotation with respect to the spectacle lens, but in the case of a progressive lens, the power differs depending on the passing point, and its position changes slightly. Since the amount of change is also small compared to the object distance, the position of the entrance pupil is at the point O ′ on the extension line of PQ, and it can be assumed that PO = PO ′.

In order to obtain an accurate PSF, it is important to divide the entrance pupil into a large number of uniformly distributed small areas. As shown in FIG. 8, there are two types of division methods, that is, lattice division and ring zone division.
The grid division gives good uniformity, but only 70% of the planned rays can be traced due to the useless parts at the four corners. On the other hand, in the zone division, a ray of a book can be traced by each zone, and the phase angle of the zone can be adjusted to improve the spot uniformity. In this embodiment, the ring zone division method is adopted.

As described above, the PSF can be obtained by tracing a large number of light rays emitted from the object point and passing through the equally divided points of the entrance pupil, and counting the spots on the retina surface. However, this PSF is a function of the retina position (y _m, z _m), tangent of rotation angle
A convolution operation cannot be directly performed with a convoluted retinal image having coordinates (Ψ, ζ). Therefore, it is necessary to find the angle of the incident ray corresponding to the retina position. In most cases (y _m , z _m ) is close to the optical axis, so the paraxial optics equation can be applied. In other words, as shown in FIG. _{9, (y m, z m} ) deflection angle from the optical axis of the incident light corresponding to (β _m, γ _m) is tan _m = y _m
/ F, tan γ _m = z _m / f. Here, f is the focal length of the eyeball. Strictly speaking, the relational expression between the incident angle and the retina position changes depending on the object distance and the adjustment state of the eye, but in the case of the eye, since the object distance is much longer than the focal length, it can be regarded as infinity.

Considering the case where the arbitrary object point P in FIG. 7 is viewed, the angle from the gaze line corresponding to the retina position (y _m , z _m ) is further calculated from the direction angle (β, γ) of P by (β _m , γ _m ). Note that the angle is generally
It is not (β + β _m , γ + γ _m ), and it is necessary to obtain it using the law of Listing convolution. In this way, PSF (y _m , z _m ) on the retina obtained by ray tracing is calculated as PS on the incident ray angle coordinate.
It can be converted into F (Ψ, ζ), and convolution with the brightness distribution of the object is possible. FIG. 10 shows the PSF acquisition method 1 as a summary of the PSF acquisition procedure described above.

(4) Convolution step In this step, the original distortion image including distortion by the lens system created in the original distortion image creation step and the PSF of each pixel obtained in the PSF acquisition step are convoluted to obtain a virtual image. This is a step of creating a convoluted retinal image when a virtual object placed in a three-dimensional space is viewed through a specific position of a lens system with a specific position and an eye in the direction of the line of sight. The convolution operation is performed as follows, for example. The light intensity distribution of the ideal image on the image plane is f (μ,
ν) and the PSF at the point (μ, ν) is p (x, μ, u, v), the light intensity at the point (μ, ν) on the retina is expressed by the following formula.

[0037]

[Equation 1]

Here, p (u, v, u-μ, v-ν) is each point
It is the PSF value at a point (u-μ, v-ν) away from (u, v). Further, a is the spread radius of the PSF. By calculating the light intensity at all points on the retina using this equation, a still image of the convoluted retinal image can be obtained. Figure 1
1 is a diagram showing an example of a still image of a convoluted retinal image obtained by the method of Example 1. FIG. This example is 0.00D for right eye
Through the near-use part of the 2.00D progressive lens for eyeglasses (HOYALUX GP; product name of Hoya Co., Ltd.), the printed matter on the table is 333
This is a convoluted retinal image when viewed at a distance of mm. Left and right field of view is 50
Up and down 38.5 °. The circle in the upper right corner is a display for indicating the lens passing point position of the central line of sight. Although the position of this passing point cannot be identified in the figure, it is indicated by a red dot in the circle. This circle represents the contour of the lens, the point attached to the center of the circle indicates the geometric center of the lens, and the circles above and below the geometric center indicate the distance measurement point (top) and the near measurement point (bottom). Show. The mark with the R letter on the back indicates the right lens. Figure 1
In the example of 1, the lens passing point of the central line of sight is the near measurement point (circle below)
This is an example of the case above. It can be seen that the blurring and distortion on the left and right are actually reproduced.

According to this embodiment, it is possible to obtain an image in which blurring or distortion perceived when viewed through a lens system such as a progressive multifocal lens is approximately reproduced. That is, the whole field of vision is clearly perceived by a healthy naked eye, but when a presbyope wears a progressive multifocal lens, only a part of the field of vision is clearly visible, and other parts are blurred or distorted. Looks like According to this embodiment, an image that such a presbyope will perceive can be reproduced as an image. Therefore, by displaying the obtained image on the display device, the designer who is not presbyopia can confirm the appearance of the progressive multifocal lens designed by himself from the viewpoint of the wearer, which is the most desirable evaluation. It will be possible.

(Embodiment 2) In this embodiment, a large number of still images of the revolving retinal image in the first embodiment are created in time series while changing the position of the eye and the direction of the line of sight to obtain a moving image of the revolving retinal image. Is. Therefore, in this embodiment, when the original image is created, a step of creating a story of how to change the eye position and the line-of-sight direction in time series, and the steps of creating each story obtained in time series. 12 is basically the same as that of the first embodiment except that a step of editing a still image to make a moving image is added.
The figure showing the overall flow is shown in FIG. It goes without saying that the story also needs a story of the lens passing point. In addition, as a method of creating a story, a smooth line-of-sight movement can be realized by using a spline interpolation method instead of defining the eye position, the line-of-sight direction, and the lens passing point at all times.

By the way, in this embodiment, the process that requires the longest time for the calculation process is the PSF acquisition process. In particular, when the lens system is a progressive multifocal lens, the PSFs in all the line-of-sight directions are different, so it is necessary to obtain the PSFs for all the pixels. For example, in an 800 × 600 image, if the number of rays to be traced when calculating the PSF is set to 400 (never too many), ray tracing calculations will be performed 192,000,000 times in total. Depending on the complexity and number of surfaces of the optical system, assuming that the computer has a computing power of 3,000 per second, it will be 64,000 seconds, or 17 hours 46 minutes and 40 seconds. This is the calculation time when the necessary time such as the convolution operation is not taken into consideration. Since this simulation aims at moving images, 30 frames per second must be simulated to create 1800 images in order to create one minute of video. Then, the ray tracing time alone is 32,0
00 hours = 1333 days, about 3 years and 8 months. Therefore, it is theoretically possible to find PSF only by ray tracing, but it is not very realistic considering the huge amount of calculation.

Therefore, the method considered is not to perform ray tracing on all object points, but to perform ray tracing only on sample points and obtain the other points by spline interpolation. The arbitrary point A in space may be expressed by Cartesian coordinates (x, y, z), but in the case of glasses, the distance from the eye is important,
It is more appropriate to express it by the reciprocal D ₁ of the distance from the turning point and the tangent ψ, ζ of the azimuth angle. That is,

[0043]

[Equation 2]

It is An arbitrary ray emanating from point A, that is, tentative
Arbitrary point (y_p, z_p) Traces rays that pass through
Ray data obtained by (incident light corresponding to the intersection on the retina
Line tk_m, cf_m, Optical path length, etc.) is D₁, ψ, ζ, y_p, z_p
Is a function of. That is, tk_m= F_t(D₁, ψ, ζ, y_p,
z_p), Ck_m= F_c(D₁, ψ, ζ, y_p, z_p), Pk_m= F_p
(D ₁, ψ, ζ, y_p, z_p). Color collection
When considering the difference, it is advisable to add a wavelength dimension. Each strange
Number D₁, ψ, ζ, y_p, z_pAppropriate within each predetermined range
Sample points are set at numbers and positions, and all points on the 5-dimensional grid are
Ray tracing is performed in advance for the sample points
If you obtain the data, you can find an arbitrary point within the predetermined range (5-dimensional box).
Current ray data by spline interpolation
You can

Next, the speedup of the spline interpolation calculation will be examined. One-dimensional spline interpolation is

[Equation 3] It is represented by. Here, i is the node number of each dimension, C _i is its coefficient, and n is the number of sample points. N _I (x) is a basis function corresponding to the i-th node, and in the case of rank M, the i-th node and i +
It has a non-zero value in the range between the Mth node and the adjacent nodes and is represented by an m-1 degree polynomial (locality of basis function). In other words, at any point a within the domain of x, there will be at most M non-zero N _I (x). Therefore,
The interpolation formula seems to have n terms at first glance, but when x = a, it is actually a M term, and F times by M multiplications and M additions.
(a) is obtained. Five-dimensional spline interpolation is

[0046]

[Equation 4]

It is represented by Here, i, j, k, l, and m are the node numbers of the respective dimensions, and each changes by the number of sample points. In other words, the number of terms is the product of the number of sample points in each dimension. However, due to the locality of the basis functions described above, for a given point, the number of non-zero terms is the product of the ranks of each dimension. If the spline rank of each dimension is 4, then the number of terms is 4 ⁵ = 1024. In other words, in one interpolation calculation,
1024 times, multiplication 1024 × 5 = 5120 times. In general, the number of multiplications required for the nj-dimensional M-th order spline interpolation calculation is nj × M ^nj , and the calculation load rapidly increases as the number of dimensions increases. However, the above formula

[0048]

[Equation 5]

By rewriting to, it is possible to reduce a little.
This is a one-dimensional interpolation nest structure, and the order of dimensions can be changed freely. Both multiplication and addition
4 + 4 x (4 + 4 x (4 + 4 x 4))) = 1364 times, almost 1
Calculation time of / 3 is enough. Generally, the number of multiplications required for the nj-dimensional Mth-order spline interpolation calculation is

[0050]

[Equation 6]

It is Even if such a measure is adopted,
It is still computationally expensive and not practical. In general, it will be difficult to further reduce the calculation time of the multidimensional spline interpolation as compared with the above method. However, if you want the PSF,
Due to its special circumstances, there are ways to shorten it further. In order to obtain the PSF of one point (D ₀ , ψ ₀ , ζ ₀ ) on the object, ray data connected to many (for example, 400) points on the entrance pupil plane (y _p , z _p plane) is necessary. The three-dimensional variable of 400 times five-dimensional spline interpolation will put the same value. If the 400 times of interpolation is performed by two-dimensional spline interpolation, the calculation time can be greatly shortened. Rewrite the five-dimensional spline interpolation formula as follows.

[0052]

[Equation 7]

This expression is given by
It shows a method of obtaining a two-dimensional space when three-dimensional variables are fixed. Where this two-dimensional spline is a point
It is called a degenerate space of (D ₀ , ψ ₀ , ζ ₀ ), and c _{l, m} is a coefficient of the degenerate spline. Of course, the nodes and basis functions of the degenerate spline are all the same as the five-dimensional spline. The number of c _{l, m} is the product of the number of sample points, and is 81 when 9 sample points are set for each of the y _p and z _p dimensions. To find each coefficient,
3D spline interpolation is used as shown in the equation. Then, using the obtained cl _{, m} , it is possible to perform the two-dimensional spline interpolation calculation of the light ray data at any one point on the y _p -z _p plane. Therefore, the PSF at the point c can be obtained by only performing 81 times of three-dimensional interpolation and 400 times of two-dimensional interpolation calculation. The number of multiplications is 81 x {4 / (4-1)} (4 ³ -1) + 400 x {4 / (4
-1)} (4 ² -1) = 14804 times, which is about 37 times per ray. The effect of reducing the amount of calculation is more remarkable than 400 times of five-dimensional interpolation. Using the above method, 1/10 of ray tracing
Ray data can be obtained at the time. FIG. 13 shows the PSF acquisition method 2 by summarizing the outline procedure of PSF acquisition described above.

Next, the parameterization of PSF will be examined. As described above, by calculating the ray data by the spline interpolation method instead of ray tracing, the calculation speed of 10 times is realized. Even so, to make a one-minute video, 3
It only reduced the time required for 8 months (44 months) to 4.4 months. In terms of processing time per frame, 64000 seconds (17
It just shortened the time from 46 minutes and 40 seconds to 6400 seconds (1 hour and 46 minutes and 40 seconds). Practically, we want to reduce the processing time per frame to a few minutes. In the current method, the calculation for obtaining the PSF takes the longest time, so shortening it is the most effective.

To obtain the PSF of a certain object point (D ₀ , ψ ₀ , ζ ₀ ) strictly, it is necessary to trace or interpolate a large number of rays and obtain the ray density thereof. Moreover, the obtained PSF is a discrete function for each pixel, and the density is also in the form of the number of rays per pixel. When the rays are concentrated (in focus)
Has a large number of rays in a small number of pixels and is close to a continuous function, but when scattered over a wide range (out of focus), the number of rays entering a unit pixel is small and the error is large. More and more rays are needed to cover it. Therefore, if the PSF is assumed to be a continuous function in advance and its parameters are applied using the ray tracing data, it is possible to escape from the above dilemma. Then, it is not necessary to obtain the parameters for all the object points, but it is possible to determine the sample points and obtain them by spline interpolation (three-dimensional).

Considering what kind of function should be used for the distribution function, most PSFs have a mountain shape, so it can be considered that the two-dimensional normal distribution is appropriate. That is,

[0057]

[Equation 8]

Here, μ and ν are deviations from the chief ray in the tk and cf directions, respectively, and σ _μ , σ _ν and ρ are parameters of the normal distribution. These parameters have the following properties. −1 <ρ <1, σ _μ > 0, σ _ν > 0, ellipse

[Equation 9] At all points (μ, ν) of

[Equation 10] Is. And the integral in that equal probability ellipse is

[Equation 11]

As shown in FIG. 14, the equiprobable ellipse is shaped by the shapes circumscribed rectangles σ _μ / σ _ν and ρ, and the radius number c
The size is decided by. Rewriting the ellipse equation into polar coordinates, the ellipse when c = 1 is

[Equation 12] Becomes If you organize it,

[Equation 13] Becomes here,

[Equation 14] Is. Thus, since A> B is surely established, γ
The maximum and minimum values of, that is, the lengths of the major and minor axes of the ellipse are

[Equation 15] The angles of the long and short axes are α and α + π / 2. These are important quantities for evaluating the direction and degree of astigmatism.

As described above, the two-dimensional normal distribution function can represent the extent of spread (σ _μ , σ _ν ), the extent of astigmatism (equal probability elliptic long-short axis ratio), and angle (angle of long axis). it can. Of course, it is not possible to faithfully represent the nearly infinite change due to the state of the PSF optical system, but it will be effective as a simplified function for expressing the PSF.

Parameters of the two-dimensional normal distribution function σ _μ , σ
Considering the method of obtaining _ν and ρ from ray data, (μ,
ν) Obtain statistical values of intersections of a large number of light rays scattered on the plane (each intersection corresponds to each division point on the entrance pupil), and a method naturally applied to σ _μ , σ _ν , ρ will come up. That is,

[Equation 16] Is. Here, N is the number of light rays, and (μ _i , ν _i ) is the intersection coordinate. [sigma] [ _{mu] 0} , [sigma] [ _{nu] 0} , and [rho] are statistics of the distribution to the last, and are not appropriate as parameters of the approximate normal distribution in many cases. FIG. 14 shows an example thereof. The mountain on the left shows the intersection density, and the mountain on the right shows the normal distribution with σ _μ0 , σ _ν0 , and ρ as parameters.

As shown in FIG. 15, when the normal distribution in which σ _μ0 , σ _ν0 , and ρ are directly applied is adopted, the principal axis direction and the major / _minor axis ratio are in accordance with the actual distribution, but the extent of the spread is actual. It is far from the distribution. Therefore, it sets an appropriate proportional coefficient k, by applying the _{σμ = kσ μ0, σ ν =} kσ ν0, very close approximation to the actual distribution can be obtained. The problem is how to determine k. Regarding this, the probability P (c) inside the equal probability ellipse and the half coefficient c
You can get a hint to the relationship curve of. Parameters _{σ μ = kσ μ0, σ ν} = kσ ν0, P normal distribution in the case of changing the [rho (c) curve _{P k (c) = 1-} exp (-c 2/2
k ² ). It suffices to determine k so that it approximates the P _r (c) curve of the actual distribution.

FIG. 16 shows P (c), P of the example of FIG._k(c),
P_rThe curve of (c) is plotted. Close to PSF distribution
The center part is especially important when seeking similarity. Therefore,
P when c is small_r(c) P that is as close as possible to the curve_k(c) wants
Good Statistics value σμ₀, Σν₀, Ρ is applied as is
Curve P (c) is the actual distribution P_rapart from (c)
Therefore, it is not suitable as an approximate distribution function. On the other hand, k = 0.65
σ_μ= Kσ_μ0, σ_ν= Kσ_ν0, ρ applied to the normal distribution
Curve P_k(c) P near the center_r(c) The part that matches the curve
It can be seen that the approximation is close to the actual distribution. Figure 1
7 is σμ = kσμ ₀, σν = kσν₀, ρ is normal distribution
It is a comparison with the distribution of.

In this embodiment, the following method is adopted in determining the value of k. First, the P _r (c) curve and P _k
(c) Determine the value of the probability P ₀ of the point A where the curves intersect. Since importance is attached to the vicinity of the center, P ₀ = 0.1 is set here. P (c)
At the point of P (c) = P ₀ on the curve,

[Equation 17] Is. If c = Cr at the point A of the Pr (c) curve, k =
It becomes Cr / C0.

Other methods (eg P_r(c) and P_kwith (c)
It is possible to minimize the difference near the center.)
The method is the simplest. In this way, the object space
One point (D₀, ψ₀, ζ₀), The PSF distribution function of
_μ, σ_ν, a two-dimensional normal distribution function with
it can. Of course you will encounter the simulation process
Σ for all object points_μ, σ_νI need to find ρ
Σ at the sample point_μ, σ_ν, ρ only in advance
And using it, σ at an arbitrary object point_μ, σ _ν, ρ
Can be obtained by spline interpolation. By that
Therefore, the calculation time can be saved significantly.

By parameterizing the PSF distribution function, the processing time per frame is changed from 1 hour 46 minutes 40 seconds to 2-1.
I succeeded in shortening it to about 0 minutes. The processing time varies because the processing time varies depending on the degree of blurring. It takes about 100 hours, or a week, to make a one-minute video. FIG. 18 shows the PSF acquisition method 3 by summarizing the outline procedure of PSF acquisition described above.

According to the second embodiment described above, in addition to the blurring and distortion perceived when viewed through a lens system such as a progressive multifocal lens, the shake when the eye position is changed or the line of sight is moved is reproduced. A moving image is obtained. Therefore, by displaying the obtained moving image on the display device, it becomes possible to make an evaluation with a sense of realism as if the user became a wearer. By displaying the point where the line of sight passes through the lens on the display face of the moving image of the convoluted retinal image, it is possible to see blurring and distortion shake while confirming the movement of the line of sight on the lens.

Next, a device for performing the simulation shown in the above embodiment will be briefly described. FIG. 19
FIG. 1 is a block diagram showing a schematic configuration of an apparatus for performing a simulation of an embodiment. As shown in FIG.
This device has a processor 61 and a read-only scale (ROM) 6
2. Main memory 63, graphic control circuit 64, display device 65, mouse 66, keyboard 67, hard disk device (HDD) 68, floppy (registered trademark) disk device (FDD) 69, printer 70, magnetic tape device 71, etc. Has been done. These elements are the data bus 72
Are joined by.

The processor 61 centrally controls the entire apparatus. The read-only memory 62 stores a program required at startup. A simulation program for performing a simulation is stored in the main memory 63. The graphic control circuit 64 includes a video memory, converts the obtained image data into a display signal and displays it on the display device 65. The mouse 66 is a pointing device for selecting various icons and menus on the display device. The hard disk device 68 stores a system program, a simulation program, etc., and is loaded into the main memory 63 after the power is turned on. Also,
Temporarily store simulation data.

Floppy disk device 69
Inputs necessary data such as original image data through the floppy (registered trademark) 69a, and saves to the floppy (registered trademark) 69a as necessary. The printer device 70 is used to print out a rotated retina image and the like. The magnetic tape device 71 is used to save the simulation data on the magnetic tape as needed.
As the device having the above basic configuration, a high performance personal computer or a general purpose computer can be used.

[0071]

As described in detail above, the simulation apparatus for the eye optical system according to the present invention is not an optical image projected on the retina surface of the eye as an image perceived by the eye through the lens system, but within the visual field. Is equipped with a convolutional retina image creating means for revolving the eyeball with respect to all object points of the object and creating a convoluted retina image defined by combining the images captured in the fovea by computer simulation. Further, the convoluted retinal image creating means is an original image creating means for creating an image having a specific viewing angle entering an eye having a specific convolutive center point as an original image, and distortion when the original image is viewed through a lens system. Distortion original image creating means for creating a distortion original image with a ray tracing method, and an eyeball by light from an object point of the original image in an optical system including a lens system and a spectacle model. PS to obtain the PSF on the retina of Dell
The F-obtaining means, the original distorted image obtained by the original distorted image creating means, and the PSF of each pixel of the original image obtained by the PSF obtaining means are convoluted to perform the convolution operation. It is characterized in that the convoluted retinal image is edited to obtain a moving image of the convoluted retinal image, and further, the PSF creating means sets a sample point at an object point to obtain a PSF, and a PSF other than the sample point is subjected to a spline interpolation method. It is characterized by using an approximation method including. As a result, when a lens system such as a progressive multifocal lens is worn, shake, distortion,
This makes it possible to obtain a simulation device for an eye optical system that can also simulate the appearance with blur.

[Brief description of drawings]

FIG. 1 is a diagram showing a flow of creating a rotated retinal image.

FIG. 2 is a diagram showing a coordinate system of a rotating retinal image.

FIG. 3 is a diagram showing a coordinate system of a convoluted retinal image when a lens system is worn.

FIG. 4 is a diagram showing optical parameters (non-accommodation state) of a Navarro model eye.

FIG. 5 is a diagram showing an accommodative force-dependent formula of a crystalline lens of a Navarro model eye.

FIG. 6 is an explanatory diagram of PSF.

FIG. 7 is a diagram showing a relationship between ray tracing and an entrance pupil.

FIG. 8 is a diagram showing a method of dividing an entrance pupil.

FIG. 9 is a diagram showing a retina position and an incident angle.

FIG. 10 is a diagram showing one PSF acquisition method.

FIG. 11 is a diagram showing an example of a still image of a revolved retinal image.

FIG. 12 is a diagram showing a flow of creating a moving image of a revolved retinal image.

FIG. 13 is a diagram showing PSF acquisition method 2;

FIG. 14 is a diagram showing an equal establishment ellipse.

FIG. 15 is a diagram showing a light density distribution and an approximate normal distribution based on σ _μ0 , σ _ν0 , and ρ.

FIG. 16 is a diagram showing curves of P (c), P _k (c) and P _r (c).

FIG. 17 is a diagram showing a light density distribution and an approximate normal distribution based on kσ _μ0 , kσ _ν0 , and ρ.

FIG. 18 is a diagram showing PSF acquisition method 3;

FIG. 19 is a block diagram showing a configuration of an apparatus for carrying out a simulation method for an eye optical system according to the present invention.

Claims (5)

[Claims] 1. A simulation device of an eye optical system for simulating the appearance when observing the outside world through a lens system arranged in front of the eye, wherein an image perceived by the eye through the lens system,
Rotation that creates a convoluted retina image that is defined as the image obtained by combining the images captured by the fovea, not the optical image projected on the retina surface of the eye, but the eyeball for all object points in the visual field. An eye optical system simulation device comprising a retinal image creating means. 2. A simulation device of an eye optical system for simulating the appearance when observing the outside world through a lens system arranged in front of the eye, wherein an image perceived by the eye through the lens system,
Rotation that creates a convoluted retina image that is defined as the image obtained by combining the images captured in the fovea with the eyeball for all object points in the visual field, rather than the optical image projected on the retina surface of the eye. The retinal image creating means includes an original image creating means for creating as an original image an image having a specific viewing angle entering an eye having a specific center of rotation, and the original image is viewed through a lens system. A distortion original image creating means for creating a distortion original image with a ray-tracing method in the case of a distortion, and an optical system consisting of a lens system and a spectacle model on a retina of an eyeball model by light from an object point of the original image. A convolution for performing a convolution operation between a PSF acquisition unit that obtains a PSF, an original distortion image obtained by the original distortion image creation unit, and a PSF of each pixel of the original image obtained by the PSF acquisition unit. Simulation device ocular optical system; and a calculation unit. 3. The apparatus for simulating an eye optical system according to claim 2, wherein the PSF acquisition unit emits light from an object point represented by each corresponding pixel and sets the entrance pupil of the eyeball model by equally dividing it. A device for simulating an eye optical system, characterized in that all data of rays passing through respective points are obtained by a ray tracing method, and PSF is obtained as a ray spot distribution density on the retina of the eyeball model or as a diffraction integral based on wave optics. . 4. The eye optical system simulation apparatus according to claim 2, wherein the PSF acquisition unit sets a finite number of object sample points in a three-dimensional object space in advance, and a finite number on the entrance pupil plane. , The ray sampling method obtains ray data by all combinations of the object sampling point and the passing point sampling point, creates spline interpolation coefficient data, and the object point representative of each pixel of the original image The ray data passing through each point obtained by evenly dividing the entrance pupil is obtained by the spline interpolation method using the previously prepared spline interpolation coefficient data, and PSF is used as the spot distribution density of rays on the retina or in wave optics. An eye optical system simulation device characterized by being obtained as a diffraction integration method based on the above. 5. The apparatus for simulating an ocular optical system according to claim 2, wherein the PSF acquisition unit approximates the PSF by a constant function and represents the PSF by its parameter, and preliminarily sets a finite number of object sampling points in the three-dimensional object space. By selecting the PSFs at all object sample points and their approximate function parameters and creating spline interpolation coefficient data, the PSF parameters for each pixel of the original image are calculated by the spline interpolation method using the previously prepared spline interpolation coefficient data. A simulation device for an eye optical system, which is characterized by finding.