JP5500478B2 - Lenticular lens, image display method, image display apparatus, and lenticular lens manufacturing method - Google Patents

Description

  The present invention relates to a lenticular lens that displays a stereoscopic image, an image display method, an image display device, and a method for manufacturing a lenticular lens.

  There are two types of stereoscopic image display devices that require glasses and those that do not. A stereoscopic image display device using a lenticular lens is known as a method that does not require glasses. FIG. 24 is a perspective view of a lenticular lens, FIG. 25 is a diagram showing a method for capturing a multi-viewpoint image, FIG. 26 is a diagram showing a method for creating a multi-viewpoint image, and FIGS. is there.

  In FIG. 24, reference numeral 2401 denotes a cylindrical lens, and a number of cylindrical lenses are arranged in parallel to constitute a lenticular lens. The flat portion 2402 of the lenticular lens is an image plane. The multi-viewpoint image printed or displayed on the image surface 2402 is viewed by the left and right eyes through the cylindrical lens 2401 to recognize the image three-dimensionally.

  One method for capturing a multi-viewpoint image is to capture an image of the subject from many directions. FIG. 25 is a diagram for capturing a multi-viewpoint image using five cameras. In FIG. 25, a subject 2501 is imaged using five cameras 2502 to 2506. The plurality of captured images have parallax with each other.

  A method of creating a multi-viewpoint image will be described with reference to FIG. In FIG. 26, reference numerals 2602 to 2606 denote images taken by the cameras 2502 to 2506 in FIG. These captured images are divided into strip images and combined into one as shown in FIG. 26 to create a multi-viewpoint image 2601. In the example of five viewpoints as shown in FIG. 25 and FIG. 26, each strip image is compressed to 1/5 in the horizontal direction and synthesized into 2601.

  27 and 28, 2701 is a cylindrical lens, and 2702 is an image plane. An image 2703 printed or displayed on the image surface 2702 is a portion corresponding to one cylindrical lens of the multi-viewpoint image 2601 in FIG. In the example of FIGS. 27 and 28, the multi-viewpoint image 2703 is shown only on the image plane corresponding to one cylindrical lens. Actually, a multi-viewpoint image is displayed on an image plane corresponding to all cylindrical lenses. The light emitted from each point on the image plane becomes substantially parallel light by the cylindrical lens and enters the right eye or the left eye. In the positions of the right eye 2704 and the left eye 2705 as shown in FIG. 27, the substantially blind light 2706 is incident on the right eye 2704, the substantially parallel light 2707 is incident on the left eye 2705, and the right eye and the left eye are mutually connected. A stereoscopic image is recognized by looking at an image with parallax.

  In addition, when the position of the right eye 2704 and the left eye 2705 is changed as shown in FIG. 28 by moving the head position, substantially parallel light 2708 is incident on the right eye 2704 and substantially parallel to the left eye 2705. Light 2709 is incident to recognize the image three-dimensionally. Moving the head changes the three-dimensional direction, and things that were not visible in FIG. 27 can be seen in FIG. 28, increasing the sense of reality. Such a multi-viewpoint image and a stereoscopic image using a lenticular lens have been reported in recent academic conferences (see, for example, Non-Patent Document 1).

  In the lenticular lenses as shown in FIGS. 27 and 28, the light emitted from different points on the image plane becomes substantially parallel light in different directions, so that the right eye and the left eye see different images and recognize a stereoscopic image. The principle of such substantially parallel light will be described analytically with reference to FIG.

  In FIG. 29, 2901 is a cylindrical lens and 2902 is an image plane. In general, a spherical lens is used, but an elliptical lens has also been proposed (see, for example, Patent Document 1). Let R be the radius of curvature near the lens center line passing through the top of the lens. The distance from the image plane 2902 to the top of the lens is T, the refractive index of the lens medium is n, and the width of one cylindrical lens is W. Let δ be the distance from the lens center line 2903 to the point of interest on the image plane. The light coming out of the image plane point and reaching the point P on the lens surface is refracted on the lens surface and emitted from the cylindrical lens 2901 with an angle β.

The distance from the lens center line 2903 of the point P is X, and the lens shape is expressed by (Equation 1). Here, m is called an elliptic coefficient. When m = 1, it represents a spherical surface, which is a special case of an ellipse. In this lens shape, the radius of curvature at the center of the lens is R.
(Expression 1) F (X) = T−mR + [(mR) ² −mX ² ] ^1/2

The angle θ of the light ray from the point of interest on the image plane to the point P is obtained by (Equation 2). The gradient of the lens curved surface at the point P is a differential coefficient of the function F (X) and is obtained by (Equation 3). The incident angle α to the lens surface is obtained by (Equation 4), and the angle β is obtained by (Equation 5) from the law of refraction on the lens surface. Here, the differential coefficient of F (X) at the point P becomes negative if X is a positive value (the algebraic angle is negative, φ <0). In order to indicate the geometric angle as a positive value, the inclination of the tangent line at the point P is represented as (−φ) in FIG.
(Equation 2) tan θ = (δ−X) / F (X)
(Equation 3) tan φ = −m · X / [(mR) ² −mX ² ] ^1/2
(Equation 4) α = θ + (− φ)
(Formula 5) sin [β + (− φ)] = n · sin α

  If a point on the image plane (distance δ from the lens center line 2903) and a refraction point P (distance X from the lens center line 2903) of the lens surface are given, then θ, φ in order from (Equation 1) to (Equation 5). , Α, β are obtained, and the direction of the light emitted from the cylindrical lens 2901 is obtained.

  Ideally, light emitted from different points on the image plane 2902 is emitted as parallel light having different emission angles from the cylindrical lens 2901. FIG. 30 shows the ideal behavior. The horizontal axis represents the position (X) where light emitted from a point on the image plane enters the lens surface, and the vertical axis represents the emission angle (β) from the cylindrical lens. As the points on the image plane (distance δ from the lens center line 2903), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light emitted from a point on the image plane corresponding to the adjacent cylindrical lens. For example, light emitted from a point on the image plane (δ = W / 4) becomes parallel light having a constant emission angle regardless of the position on the lens surface. In other words, if the lenticular lens is viewed from the emission angle, only the image of the point (δ = W / 4) is viewed. In this way, the fact that light emitted from a point on the image surface becomes parallel light with a constant emission angle regardless of the incident position on the lens surface is referred to as a lenticular effect. In reality, such an ideal outgoing light cannot be obtained, and a realistic case will be described below.

First, consider paraxial approximation with a small ray angle. In this paraxial approximation, (Equation 1) to (Equation 5) are expressed as (Equation 6) to (Equation 10), respectively. The paraxial approximation does not depend on the elliptic coefficient m, and the ellipse is almost the same as the spherical surface near the lens center line.
(Equation 6) F (X) = T
(Equation 7) θ = (δ−X) / T
(Equation 8) φ = −X / R
(Equation 9) α = θ−φ
(Equation 10) β−φ = nα

From these (Equation 6) to (Equation 10), the emission angle β in the paraxial approximation is expressed by (Equation 11). The lenticular lens effect, that is, the condition that light emitted from a point on the image plane (distance δ from the lens center line 2903) becomes substantially parallel light with a constant emission angle is that β does not depend on θ, This is the case. Further, the emission angle β at that time is expressed by (Equation 13).
(Equation 11) β = (n−1) (δ / R) − [(n−1) (T / R) −n] θ
(Equation 12) T = Rn / (n-1)
(Equation 13) β = (n−1) (δ / R)

When the lens medium is general glass or resin, the refractive index n is about 1.5, the distance T from the image surface to the top of the cylindrical lens is (Expression 14), and the emission angle β of substantially parallel light is ( (Equation 15)
(Equation 14) T = 3R
(Equation 15) β = δ / (2R)

  Next, a general case is simulated using (Equation 1) to (Equation 5). As an example, the case of a spherical lens is shown. In FIG. 29, m = 1, R = 1, T = 3, n = 1.5, and W = 1.5. These conditions satisfy (Equation 12). FIG. 31 shows the result of the simulation. The horizontal axis represents the position (X) where light emitted from a point on the image surface enters the lens surface, and the vertical axis represents the exit angle (β) emitted from the cylindrical lens. As the points on the image plane (distance δ from the lens center line 2903), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light emitted from a point on the image plane corresponding to the adjacent cylindrical lens.

  The following can be understood from FIG. Most of the light emitted from the lens center (δ = 0) on the image plane is emitted from the cylindrical lens as substantially parallel light having an angle β = 0, and the light in the peripheral portion becomes a slightly focused light. When light coming from a point on the image plane (δ = W / 4) at a distance W / 4 from the lens center line is incident on the lens plane range (−0.75 to +0.5), the angle β = 0. When the light is emitted from the cylindrical lens as approximately parallel light having 19 radians and enters the range (+0.5 to +0.75) of the lens surface, the light becomes non-parallel light. Further, when the light emitted from the point (δ = W / 2) on the image plane corresponding to the boundary between the adjacent cylindrical lenses is incident on the lens surface range (−0.75 to +0.3), the angle β = When the light is emitted from the cylindrical lens as substantially parallel light having 0.37 radians and enters the range (+0.3 to +0.6) of the lens surface, the light becomes non-parallel light. When the light enters the lens surface range (+0.6 or more) from the boundary point (δ = W / 2), the light is not emitted from the cylindrical lens due to total reflection. Comparing FIG. 30 and FIG. 31, a lot of light is relatively close to the ideal, but there is also light that deviates from the ideal.

  In order to recognize a high-quality stereoscopic image, it is important that only an image near one point on the image plane is visible when the lenticular lens is viewed from one direction. If light from many points appears to be mixed, a plurality of images are mixed and the image quality deteriorates. A case where the lenticular lens is viewed from an angle of 0.19 radians will be described with reference to FIG. In FIG. 32, the same components as those of FIG. Reference numeral 2904 denotes an eye having an angle of 0.19 radians. As can be seen from FIG. 31, most of the light emitted from the point (δ = W / 4) on the image plane is substantially parallel light having an emission angle of 0.19 radians. These are lights in a region surrounded by the light ray 2905 (solid line) and the light ray 2906 (solid line) in FIG. 32, and this substantially parallel light can be seen from the eye 2904. Light such as light ray 2907 (dashed line) emitted from a point (δ = W / 4) on the image plane has an emission angle larger than 0.19 radians and cannot be seen by the eye 2904.

  Next, the case where the lenticular lens is viewed from an angle of 0.37 radians will be described with reference to FIG. 33, the same components as those in FIGS. 29 and 32 are given the same reference numerals, and description thereof is omitted. Eye 2904 is an eye with an angle of 0.37 radians. As can be seen from FIG. 31, most of the light emitted from the point (δ = W / 2) on the image plane is substantially parallel light having an emission angle of 0.37 radians. These are lights in a region surrounded by the light beam 2908 (solid line) and the light beam 2909 (solid line) in FIG. 33, and this substantially parallel light can be seen from the eye 2904. On the other hand, part of the light from other points on the image plane also has an exit angle of 0.37 radians. For example, light ray 2910 (dashed line) exits from a point where δ = W / 4 and is emitted with an exit angle of 0.37 radians. The light beam 2910 is generated in a very narrow range as compared with the region surrounded by the light beam 2908 and the light beam 2909, and the amount of light is small. That is, when the lenticular lens is viewed from an angle of 0.37 radians, only the image near the point where δ = W / 2 is seen.

  In FIG. 31, when the change in the emission angle β is large with respect to the horizontal axis (incident position X on the lens surface), that is, when the gradient of the curve representing the emission angle is large, the light beam 2907 (dashed line) in FIG. And the light quantity is small when seen from a certain specific emission angle like the light ray 2910 (dashed line) in FIG.

  Images from many viewpoints are displayed on the image plane corresponding to one cylindrical lens. Of these multi-viewpoint images, the adjacent images are images taken by the adjacent cameras in FIG. 25, and are highly correlated with each other. However, the image near the boundary between adjacent cylindrical lenses is, for example, an image captured by the cameras 2502 and 2506 in FIG. 25, and the correlation is low. If they are mixed, the image quality deteriorates.

  Accordingly, the light having a relatively high intensity out of the light exiting from the boundary point (δ = W / 2) between adjacent cylindrical lenses and emitted from the cylindrical lens, and the smallest exit angle determines the viewing angle of the stereoscopic image. It will be a thing. The viewing angle in the case of FIG. 31 is ± 0.37 radians (± 21 degrees). The larger the viewing angle, the more stable the stereoscopic image can be obtained.

  As shown in FIG. 31, most of the light (δ> W / 2) emitted from the image plane corresponding to the adjacent cylindrical lens also becomes substantially parallel light, but as the point on the image plane becomes farther from the lens center line, The ratio of non-parallel light increases. The light emitted from the image plane corresponding to these adjacent cylindrical lenses is outside the viewing angle and does not affect the stereoscopic image within the viewing angle.

  In order to obtain a more stable stereoscopic image, a wider viewing angle is desired. One method for increasing the viewing angle is to increase the width (W) of the cylindrical lens.

  In a spherical lens, if the lens width W is increased, the gradient around the lens increases, and the angle of the light beam refracted on the lens surface changes abruptly. The emitted light is not substantially parallel light, and the effect of increasing the lens width does not appear. An elliptical shape has been proposed as a lens shape (see Patent Document 1). By making the lens shape an ellipse, the lens width W can be increased without increasing the gradient so much.

  A case of a lenticular lens having an elliptical lens shape is simulated using (Equation 1) to (Equation 5). As an example, in FIG. 29, m = 3, R = 1, T = 3, n = 1.5, and W = 2. These conditions satisfy (Equation 12). In this example, W = 2 is set to increase the viewing angle. FIG. 34 shows the result of the simulation. The horizontal axis represents the position (X) where light emitted from a point on the image plane enters the cylindrical lens surface, and the vertical axis represents the emission angle (β) from the cylindrical lens. As the points on the image plane (distance δ from the lens center line), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light from a point on the image plane corresponding to the adjacent cylindrical lens.

  The following can be understood from FIG. Most of the light from the lens center of the image plane (lens center, δ = 0) is emitted from the cylindrical lens as substantially parallel light having an angle β = 0, and light incident on the periphery of the lens becomes slightly non-parallel light. . The light emitted from a point on the image plane (δ = W / 4) at a distance W / 4 from the lens center line is not completely parallel light, but the emission angle is moderate within the range of 0.25 radians to 0.37 radians. The emitted light changes to ## EQU3 ## and approximately satisfies the lenticular effect. The light emitted from the point on the image plane (δ = W / 2) near the boundary between the adjacent cylindrical lenses also changes gradually, and the light incident on the lens surface range exceeding +0.6 is totally reflected. It is not emitted from the cylindrical lens. The smallest emission angle among the lights from the boundary point is 0.47 radians.

  Images from many viewpoints are displayed on the image plane corresponding to one cylindrical lens. Among these multi-viewpoint images, adjacent images have a strong correlation with each other, and even if they are mixed, it does not pose a big problem for image quality degradation. However, the image near the boundary between adjacent cylindrical lenses has a low correlation, and when they are mixed, the image quality deteriorates. Therefore, out of the light exiting from the boundary point (δ = W / 2) between adjacent cylindrical lenses and exiting from the cylindrical lens, the viewing angle is determined by the smallest exit angle having a relatively high intensity. . The viewing angle in the case of FIG. 34 is ± 0.47 radians (± 27 degrees). If an elliptic lens is used, the width of the cylindrical lens can be increased, and a stable stereoscopic image with a large viewing angle can be obtained.

  For reference, FIG. 35 shows a simulation result using (Equation 1) to (Equation 5) in the case where the elliptical cylindrical lens width is not increased. Here, m = 3, R = 1, T = 3, n = 1.5, and W = 1.5 so that (Equation 12) is satisfied. The outgoing angle of light from the boundary point (δ = W / 2) between adjacent cylindrical lenses, that is, the viewing angle is ± 0.36 radians (± 21 degrees). The viewing angle does not increase just by using an elliptic lens. If an elliptic lens is used, the width of the cylindrical lens can be increased and the viewing angle can be increased.

  When the lenticular lens is viewed from a certain direction, the right or left eye recognizes a three-dimensional image by looking only at the image from one viewpoint among the multi-viewpoint images included in the width of one cylindrical lens. For example, in the case of FIGS. 27 and 28, an image from only one viewpoint among the five multi-view images (2703) is viewed. Accordingly, since one image is assigned to the width W, the stereoscopic image becomes rougher if the width W of the cylindrical lens is larger, and the resolution is higher as W is smaller. I want to increase the viewing angle without increasing the cylindrical lens width W as much as possible.

  Another way to increase the viewing angle is to increase the refractive index of the lens medium. If the refractive index is increased, the viewing angle can be increased without increasing the cylindrical lens width W. As can be seen from the exit angle equation (Equation 13) in paraxial approximation, the exit angle increases as the refractive index n of the medium increases. Recently, a glass having a high refractive index and capable of being molded has been developed. Glass having a refractive index of about 1.65 is relatively easy to obtain (for example, see Non-Patent Document 2).

  FIG. 36 shows the result of simulation using (Equation 1) to (Equation 5) in the case of a spherical lens having a refractive index n = 1.65. Here, m = 1, R = 1, T = 2.54, n = 1.65, and W = 1.5, and these conditions satisfy (Equation 12). The horizontal axis represents the position (X) where light emitted from a point on the image plane enters the lens surface, and the vertical axis represents the emission angle (β) from the cylindrical lens. As points on the image plane (distance δ from the lens center line 2903 in FIG. 29), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light from a point on the image plane corresponding to the adjacent cylindrical lens.

  From FIG. 36, it is understood that the viewing angle can be expanded to ± 0.45 radians (± 26 degrees) in a spherical cylindrical lens having a refractive index n = 1.65 and a lens width W = 1.5.

  FIG. 37 shows the result of simulation using (Equation 1) to (Equation 5) for an elliptic lens having a refractive index n = 1.65. Here, m = 3, R = 1, T = 2.54, n = 1.65, W = 1.5, and these conditions satisfy (Equation 12). The horizontal axis represents the position (X) where light emitted from a point on the image plane enters the lens surface, and the vertical axis represents the emission angle (β) from the cylindrical lens. As points on the image plane (distance δ from the lens center line 2903 in FIG. 29), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light from a point on the image plane corresponding to the adjacent cylindrical lens.

  From FIG. 37, the elliptical lens is slightly different from the spherical lens, but behaves very similar, and the viewing angle is ± 0.47 radians (± 27 degrees).

  As can be seen from FIGS. 36 and 37, when glass having a refractive index of about 1.65 is used, the viewing angle is the same as when the width W is increased without increasing the cylindrical lens width W (W = 2). Can be expanded. That is, a lenticular lens having a high resolution and a large viewing angle can be configured.

  As shown in FIG. 38, when the image surface is arranged on the lens side and the observation side is a flat surface, a stereoscopic image can be recognized as in FIGS. 27 and 28 (see, for example, Patent Document 2 and Patent Document 3). . In FIG. 38, 3801 is a cylindrical lens, and 3802 is an image plane. An image 3803 printed or displayed on the image surface 3802 is a portion corresponding to one cylindrical lens of the multi-viewpoint image 2601 in FIG. In the example of FIG. 38, the multi-viewpoint image 3803 is shown only on the image plane corresponding to one cylindrical lens. Actually, a multi-viewpoint image is printed or displayed on an image plane corresponding to all the cylindrical lenses. The light emitted from each point on the image plane becomes substantially parallel light by the cylindrical lens and enters the right eye or the left eye. Substantially non-transparent light 3806 is incident on the right eye 3804, and substantially parallel light 3807 is incident on the left eye 3805, and the right eye and the left eye recognize the images with parallax and recognize them in a three-dimensional manner.

  The lenticular lens shown in FIG. 38 is called an inverted lenticular lens, and the lenticular lenses shown in FIGS. 27 and 28 are called erect lenticular lenses. In the case of an inverted lenticular lens, as in the case of an erect lenticular lens, the light emitted from different points on the image plane becomes substantially parallel light in different directions, so that different images can be seen by the right eye and the left eye. Can be recognized.

Although a detailed simulation is not shown here, the same can be said for an inverted lenticular lens as shown in FIG. That is, if glass having a high refractive index is used, an inverted lenticular lens having a high resolution and a large viewing angle can be constructed without increasing the cylindrical lens width.
JP-A-6-308634 Japanese Unexamined Patent Publication No. 7-199382 Japanese Patent Laid-Open No. 9-189883 Proceedings of 3D image conference 2005 (July 7-8, 2005, Tokyo) Nikkei Electronics September 13, 2004 issue 79 pages

  If glass having a high refractive index is used, a lenticular lens capable of displaying a stereoscopic image with a high resolution and a large viewing angle can be realized. In general, a lenticular lens can be manufactured by a process such as molding. However, the manufacturing process using glass has low mass productivity and high cost. In addition, glass is likely to break.

  An object of the present invention is to solve the above-mentioned conventional problems, and to provide a lenticular lens that can display a stereoscopic image with a large viewing angle and a high resolution, has high productivity, and is difficult to break. It is another object of the present invention to provide an image display method using a lenticular lens, an image display device, and a method for manufacturing a lenticular lens with high mass productivity.

  In order to solve the above-mentioned conventional problems, the lenticular lens of the present invention has a convex lens portion formed in an array on a transparent plate, the refractive index of the transparent plate is n1, and the refractive index of the convex lens portion is n2. In this case, n2> n1. As a result, a lenticular lens that achieves a stereoscopic image with a large viewing angle and high resolution is obtained.

  In the lenticular lens of the present invention, it is preferable to form a resin layer between the transparent plate and the convex lens portion. This can improve the adhesion between the convex lens portion and the transparent plate.

In the lenticular lens of the present invention, an N-layer transparent layer is formed on the image surface, a convex lens portion is formed in an array on the N-layer transparent layer, and an i-th transparent layer from the image surface is formed. The refractive index is ni, the thickness of the i-th transparent layer from the image plane is di, the refractive index of the convex lens portion is n (N + 1), and the thickness of the lens center of the convex lens portion is d (N + 1). , I has a value of 1 to N, and when the radius of curvature near the center of the convex lens is R,
d1 / n1 + d2 / n2 +... + dN / nN + d (N + 1) / n (N + 1)
= R / [n (N + 1) -1]
It is characterized by satisfying the relation of As a result, a lenticular lens that achieves a stereoscopic image with a large viewing angle and high resolution is obtained.

  In the lenticular lens of the present invention, it is preferable that the convex lens portion is made of a resin in which fine particles are dispersed. By using a resin, a lenticular lens that improves mass productivity such as molding, reduces manufacturing costs, and is difficult to break is obtained. Moreover, even if light scattering occurs due to fine particles, the use of the resin only in the convex lens portion prevents a decrease in transmittance.

  In the lenticular lens of the present invention, it is preferable that the convex lens portion is an aspherical surface. As a result, the gradient of the lens surface is reduced, the thickness of the convex lens portion made of the resin is reduced, and the transmittance is further prevented from decreasing.

  The first image display method of the present invention includes a transparent plate having convex lenses formed in an array on one side, an image surface, and the adjacent convex lens when printing or displaying a multi-viewpoint image on the image surface. It is characterized in that no image is displayed on the image plane corresponding to the boundary. As a result, the influence of the image plane corresponding to the adjacent convex lens is reduced, and a stable stereoscopic image is obtained.

  In addition, the second image display method of the present invention includes a transparent plate having convex lenses formed in an array on one side, an image surface, and when the multi-viewpoint image is printed or displayed on the image surface, the transparent image The outer peripheral part of the plate displays the multi-viewpoint image centering on the outer peripheral side from the center of the convex lens. This makes it possible to enlarge the eye position for obtaining a stable stereoscopic image.

  The image display device of the present invention is characterized by having a part for displaying a stereoscopic image and a part for displaying a planar image. As a result, it is possible to always display a high-resolution planar image and display explanatory characters relating to the stereoscopic image.

  In the first method for producing a lenticular lens of the present invention, a transparent plate and a mold having a lens array shape are opposed to each other, a first ultraviolet curable resin is inserted between the transparent plate and the mold, To cure the first ultraviolet curable resin. With this manufacturing method, a lenticular lens having a high resolution, a large viewing angle, and being hard to break can be manufactured at low cost.

  In the second method for producing a lenticular lens of the present invention, a second ultraviolet curable resin layer is formed on a transparent plate, and a mold having a lens array shape is opposed to the second ultraviolet curable resin layer, A first ultraviolet curable resin is inserted between the second ultraviolet curable resin layer and the mold, and the first and second ultraviolet curable resins are cured by irradiating ultraviolet rays. By this manufacturing method, a lenticular lens having high resolution, a large viewing angle, hardly cracking, and improved adhesion between the convex lens portion and the transparent plate can be manufactured at low cost.

  According to a third method of manufacturing a lenticular lens of the present invention, a mold having a lens array shape is pressed against a resin sheet to produce a resin sheet having a lens array formed on one side, and the third is formed on a transparent plate. Forming an ultraviolet curable resin layer, overlaying the resin sheet on which the lens array is formed on the third ultraviolet curable resin layer, and irradiating ultraviolet rays to cure the third ultraviolet curable resin. And By this manufacturing method, a lenticular lens having high resolution, a large viewing angle, hardly cracking, and improved adhesion between the convex lens portion and the transparent plate can be manufactured at low cost.

  In the first or second method for producing a lenticular lens of the present invention, the first or second ultraviolet curable resin is preferably a resin in which fine particles are dispersed. As a result, a lenticular lens using a resin having a high refractive index can be manufactured.

  In the third method for producing a lenticular lens of the present invention, it is preferable that the resin sheet on which the lens array is formed is a resin in which fine particles are dispersed. Thus, a lenticular lens using a resin having a high refractive index can be manufactured.

  According to the lenticular lens of the present invention, it is possible to provide a stereoscopic image with high resolution and a large viewing angle. In addition, since the lenticular lens has high productivity and is difficult to break, it is possible to provide a cheap and safe stereoscopic image. According to the image display method of the present invention, the range in which a stereoscopic image can be viewed can be enlarged, and a stable stereoscopic image can be provided. Further, according to the image display device of the present invention, it is possible to provide an image display device that has a portion for displaying a planar image and can display fine characters and the like. Furthermore, according to the method for manufacturing a lenticular lens of the present invention, a lenticular lens having a high resolution, a large viewing angle, and being hard to break can be manufactured at low cost.

Sectional drawing of the printed matter of a stereo image. Sectional drawing of the display of a stereo image. FIG. 4 is an analytical explanatory diagram when the refractive index of only the lens portion is high in the present invention. The analytical explanatory view in case the transparent board has a multilayer structure in the present invention. The simulation result of the spherical cylindrical lens in Embodiment 1 of this invention. Explanatory drawing of the shape of an aspherical cylindrical lens. The simulation result of the elliptical cylindrical lens in Embodiment 2 of this invention. The simulation result of the hyperbolic cylindrical lens in Embodiment 3 of this invention. Sectional drawing of the concrete lenticular lens based on Embodiment 3 of this invention. Explanatory drawing of the image display method using the lenticular lens of Embodiment 1 thru | or 6 of this invention in Embodiment 7 of this invention. Explanatory drawing of the image display method using the conventional lenticular lens in Embodiment 7 of this invention. The figure which shows the relationship between the position of an eye and a light ray in the case of appreciating the stereo image using the lenticular lens of Embodiment 1 thru | or 6 of this invention. The figure which shows the relationship between the position of an eye and light rays in the case of appreciating the stereo image using Embodiment 1 thru | or 6 of this invention in Embodiment 8 of this invention. The figure which shows the relationship between the position of the eye and light in the case of appreciating the stereo image using the conventional lenticular lens in Embodiment 8 of this invention. The simulation result of the hyperbolic cylindrical lens using resin with higher refractive index in Embodiment 9 of this invention. The simulation result of the hyperbolic cylindrical lens in the case of the resin with higher refractive index and larger lens width in Embodiment 10 of this invention. Sectional drawing of the inverted lenticular lens in which only the lens part in Embodiment 11 of this invention was made from resin with a high refractive index. The block diagram of the image display apparatus which has the part which displays the planar image, and the part which displays a stereo image in Embodiment 12 of this invention. The perspective view of the fly's eye lens in Embodiment 13 of this invention. Explanatory drawing of the 1st manufacturing method of a lenticular lens in Embodiment 14 of this invention. Explanatory drawing of the 2nd manufacturing method of a lenticular lens in Embodiment 15 of this invention. Explanatory drawing of the 3rd manufacturing method of a lenticular lens in Embodiment 16 of this invention. Explanatory drawing which forms a lens array using the roller in the single side | surface of the resin sheet in Embodiment 17 of this invention. The perspective view of the conventional lenticular lens. The block diagram of the conventional image pick-up from multiple viewpoints. The figure which shows the preparation method of a multiview image. The principle figure of the stereoscopic vision with respect to the position of the right and left eyes using the conventional lenticular lens. The principle figure of the stereoscopic vision when the position of the right and left eyes using the conventional lenticular lens changes. FIG. 6 is an analytical explanatory diagram of a conventional cylindrical lens. The figure which shows the angle of an ideal emitted light. Simulation results of a conventional spherical cylindrical lens. Explanatory drawing of the light emitted from the point of the image surface at the time of using the conventional spherical cylindrical lens. Explanatory drawing of the light emitted from the point of the image surface corresponded to the boundary of an adjacent lens at the time of using the conventional spherical cylindrical lens. Simulation results when using a conventional elliptical cylindrical lens and increasing the lens width. Simulation results when a conventional elliptic cylindrical lens is used and the lens width is not increased. Simulation results when using a conventional spherical cylindrical lens and increasing the refractive index. Simulation results when using a conventional elliptic cylindrical lens and increasing the refractive index. The principle figure of the stereoscopic vision with respect to the position of the right and left eyes using the conventional inverted lenticular lens.

Explanation of symbols

DESCRIPTION OF SYMBOLS 101 Transparent plate 102 High refractive index lens part 103 Image display part 201 Transparent board 202 High refractive index lens part 203 Image display part 204 Transparent panel 301 Transparent board 302 High refractive index lens part 303 Image surface 401 Multilayer transparent board 402 High refractive index lens 403 Image surface 601 Spherical surface 602 Aspherical surface 603 Image surface 901 Transparent plate 902 High refractive index lens portion 903 Image surface 904 Lens center (bus line)
905 Boundary between transparent plate and lens unit 1001 Transparent plate 1002 High refractive index lens unit 1003 Image plane 1006 Displayed image 1101 Lenticular lens 1102 Image plane 1103 Displayed image 1201 Transparent plate 1202 High refractive index lens unit 1203 Image plane 1204 Eye 1205 Center image 1208 Left end image 1209 Right end image 1401 Lenticular lens 1402 Image plane 1403 Eye 1404 Center image 1405 Left end image 1406 Right end image 1701 Transparent plate 1702 High refractive index lens portion 1703 Image plane 1801 Image display device 1802 Lenticular Lens 1803 Plane image 1901 Single lens 1902 Fly eye lens 2001 Transparent plate 2002 Mold 2003 First UV curable resin 2004 UV lamp 200 UV 2006 Second UV curable resin 2201 Resin sheet 2202 Mold 2203 Transparent plate 2204 Third UV curable resin 2205 UV lamp 2206 UV 2301 Resin sheet 2302 Roller 2401 Cylindrical lens 2402 Image surface 2501 Subject 2502 Camera 2503 Camera 2504 Camera 2505 Camera 2506 Camera 2601 Multi-viewpoint image 2602 Captured image 2603 Captured image 2604 Captured image 2605 Captured image 2606 Captured image 2701 Cylindrical lens 2702 Image surface 2703 Multi-viewpoint image 2704 Right eye 2705 Left eye 2706 Substantially parallel light 2707 Substantially parallel light 2709 Nearly parallel light 3801 Cylindrical lens 3802 Image plane 3803 Multi-viewpoint image 3804 Right 3805 eye 3806 a substantially parallel light 3807 substantially parallel light

  The basic configuration and embodiments of the lenticular lens of the present invention will be described below with reference to the drawings. At that time, the same analysis method as in the conventional example is used.

  As described in the conventional example, if a general lens medium having a refractive index of about 1.5 is used, it is necessary to increase the cylindrical lens width in order to expand the viewing angle. However, if the lens width is increased, the resolution decreases. If a lens medium having a high refractive index is used, a stereoscopic image having a high resolution and a large viewing angle can be provided without increasing the lens width. If glass is used as a lens medium having a high refractive index, mass productivity is low, manufacturing costs are high, and there is a possibility of cracking.

  Therefore, “nanocomposite resin” in which fine particles having a high refractive index are dispersed is used as a resin having a high refractive index. An ultraviolet curable resin is used as the base material resin, and fine particles of a dielectric such as titanium oxide, zirconium oxide, zinc oxide, or aluminum oxide having a diameter of 10 nanometers or less are used as the fine particles. A resin having a refractive index of 1.65 or more can be synthesized by dispersing fine particles of one kind or two or more kinds of these dielectrics. If fine particles are mixed in the resin, the transmittance is reduced due to scattering by the fine particles. Therefore, when nanocomposite resin is used, the smallest possible resin thickness is desired.

  FIG. 1 shows a cross-sectional view of a printed matter of a stereoscopic image. In FIG. 1, a cylindrical lens portion 102 is formed on a transparent plate 101, and a multi-viewpoint image (2601 in FIG. 26) is printed on a plane portion of the transparent plate 101 opposite to the cylindrical lens forming side. A high refractive index resin is used only for the cylindrical lens portion.

  FIG. 2 shows a cross-sectional view of a stereoscopic image display. A cylindrical lens unit 202 is formed on the transparent plate 201, and a display is arranged on the opposite side of the transparent plate 201 from the cylindrical lens forming side. Reference numeral 203 denotes an image display unit of the display, and reference numeral 204 denotes a transparent panel. The image display unit 203 includes a liquid crystal layer, a plasma discharge unit, an organic EL layer, and the like. A multi-viewpoint image (2601 in FIG. 26) is displayed on the image display unit 203. A high refractive index resin is used only for the cylindrical lens portion.

  As shown in FIGS. 1 and 2, it will be analytically explained that the viewing angle can be expanded by using a high refractive index resin only for the cylindrical lens portion. FIG. 3 is a diagram schematically showing FIGS. 1 and 2. In FIG. 3, 301 is a transparent plate made of a general resin (refractive index is about 1.5), 302 is a cylindrical lens portion made of high refractive index resin, 303 is an image plane, 304 is a lens center line, 305 Is a boundary between the transparent plate 301 and the cylindrical lens portion 302.

  When the stereoscopic image printed matter of FIG. 1 is represented using FIG. 3, a multi-viewpoint image is printed on the image surface 303, and the transparent plate 301 of FIG. 3 corresponds to the transparent plate 101 of FIG. When the stereoscopic image display of FIG. 2 is represented using FIG. 3, a multi-viewpoint image is displayed on the image plane 303. Further, when the transparent plate 201 and the transparent panel 204 are made of general glass or plastic, their refractive indexes are almost the same and can be considered as one. Therefore, the transparent plate 301 corresponds to a plate in which the transparent plate 201 and the transparent panel 204 are integrated. When a nanocomposite resin is used as the high refractive index resin, the resin thickness can be reduced by the configuration shown in FIGS. 1 to 3 to prevent a decrease in transmittance.

  In FIG. 3, T is the distance from the image plane 303 to the top of the cylindrical lens unit 302, S is the distance from the image plane 303 to the boundary 305, and R is the radius of curvature near the lens center line 304. Further, the refractive index of the transparent plate 301 is n1, the refractive index of the cylindrical lens unit 302 is n2, and the width of one cylindrical lens unit is W. Let P1 be a point where light emitted from a point of interest on the image plane 303 (distance δ from the lens center line 304) is incident on the boundary 305, and P2 be a point where the light is emitted from the cylindrical lens unit 302.

  In order to obtain the lenticular effect with the configuration of FIG. 3, it is necessary to optimize the refractive index and thickness of the transparent plate 301 and the cylindrical lens portion 302. That is, optimization of T, S, n1, n2, etc. in FIG. 3 is necessary.

In FIG. 3, it is assumed that the distance from the lens center line 304 is X and the lens shape is represented by a function F (X). The angle θ of the light ray from the point of interest (lens center line 304 to δ) on the image plane 303 toward the point P1 (X1, S) on the boundary 305 is obtained by (Equation 16), and the incident angle to the boundary 305 is also θ It is. The angle α is obtained by (Equation 17) from the law of refraction at the boundary 305, and the light beam from the point P1 to the point P2 is given by the equation (Equation 18). The distance X2 from the lens center line 304 of the point P2 is obtained by solving the equation (Equation 19). The gradient of the lens curved surface at the point P2 is a differential coefficient of the function F (X) and is obtained by (Equation 20), and the angle ν is obtained by (Equation 21) from the law of refraction on the lens surface. Here, the differential coefficient of F (X) at the point P2 becomes negative if X is a positive value (the algebraic angle is negative, φ <0). In order to indicate the geometric angle as a positive value, in FIG. 3, the inclination of the tangent at the point P2 is represented as (−φ).
(Equation 16) tan θ = (δ−X1) / S
(Equation 17) n1 · sin θ = n2 · sin α
(Equation 18) YS = −cot α · (X−X1)
(Equation 19) F (X) = S-cot α · (X−X1)
(Equation 20) tanφ = dF (X) / dX
(Expression 21) sin (ν−φ) = n 2 · sin (α−φ)

  Given a function F (X), a point on the image plane (distance δ from the lens centerline 304), and a refraction point P1 (distance X1 from the lens centerline 304) on the boundary 305, (Equation 16) to (Equation 21). ), Θ, α, X2, φ, and ν are obtained in order, and the direction of light emitted from the cylindrical lens unit 302 is obtained.

First, consider paraxial approximation with a small ray angle. In paraxial approximation, the lens shape F (X) is (Equation 22). The radius of curvature near the lens center line 304 is R, and the gradient of the lens curved surface is given by (Equation 23). In the paraxial approximation, (Equation 16), (Equation 17), and (Equation 19) to (Equation 21) are expressed as (Equation 24) to (Equation 28), respectively.
(Equation 22) F (X) = T
(Equation 23) dF (X) / dX = −X / R
(Equation 24) θ = (δ−X1) / S
(Equation 25) n1 · θ = n2 · α
(Equation 26) T = S− (X2−X1) / α
(Equation 27) φ = −X / R
(Expression 28) ν−φ = n 2 · (α−φ)

From these (Equation 22) to (Equation 28), the exit angle ν in paraxial approximation is expressed by (Equation 29). The lenticular lens effect, that is, the condition that light emitted from a point on the image plane (distance δ from the lens center line 304) becomes substantially parallel light with a constant emission angle is that ν does not depend on θ, This is the case. Further, the emission angle ν at that time is expressed by (Equation 31). Here, H = T−S.
(Expression 29) ν = (n2-1) (δ / R)
+ [N1- (n2-1) (n1 · H + n2 · S) / (n2 · R)] θ
(Expression 30) n1 · H + n2 · S = n1 · n2 · R / (n2-1)
(Equation 31) (nu) = (n2-1) ((delta) / R)

  If n1 = n2 = n in FIG. 3, FIG. 3 has the same configuration as FIG. 29, and (Equation 29) through (Equation 31) are the same as (Equation 11) through (Equation 13). Here, the angle ν in FIG. 3 is the same as the angle β in FIG. 29.

Further, the distance between the boundary line between adjacent cylindrical lenses and the image plane 303 needs to be larger than the thickness S of the transparent plate 301. Otherwise, the boundary portion between adjacent cylindrical lenses will not have a high refractive index. The condition is given by (Equation 32).
(Expression 32) F (W / 2)> S

  If the refractive indexes of the transparent plate 201 and the transparent panel 204 in FIG. 2 are approximately the same, they can be handled integrally as in the transparent plate 301 in FIG. However, if the refractive indexes of the transparent plate 201 and the transparent panel 204 in FIG. 2 are different, the transparent plate 301 in FIG. 3 must be handled as a multilayer plate. In addition, in FIG. 2, even when there is an air layer (refractive index is 1) between the transparent plate 201 and the transparent panel 204, it is a multilayer plate in which the air layer is considered as one layer. FIG. 4 shows a case where a multilayer plate is provided between the image plane and the cylindrical lens portion. In FIG. 4, 401 is a multilayer board, 402 is a cylindrical lens unit, and 403 is an image plane. From the image 403, the thickness of the i-th layer is di, and the refractive index of the i-th layer is ni. Also, the ray angle in the i-th layer is θi, and the distance from the lens center line 404 of the refraction point at the boundary between the i-th and (i + 1) -th layers is X (i + 1).

Similar to the relational expressions (Equation 22) to (Equation 28) in the paraxial approximation in FIG. 3, the relational expressions (Equation 33) to (Equation 38) are obtained in the paraxial approximation in FIG. 4. Although FIG. 4 shows a three-layer structure, the relational expression of the N-layer structure is shown by expanding to a general case.
(Expression 33) F (X) = T
(Expression 34) dF (X) / dX = −X / R
(Expression 35) X (i + 1) = Xi−di · θi
(Equation 36) n (i + 1) · θ (i + 1) = ni · θi
(Expression 37) φ = −X (N + 1) / R
(Expression 38) ν−φ = n (N + 1) · [θ (i + 1) −φ]

From (Equation 33) to (Equation 38), ν of paraxial approximation is (Equation 39). The condition that the lenticular lens effect, that is, the light emitted from a point on the image plane (distance X1 from the lens center line 404) becomes substantially parallel light with a constant emission angle is that ν does not depend on θ1, and is expressed by (Equation 40) This is the case. Further, the emission angle ν at that time is expressed by (Equation 41).
(Equation 39) ν = [n (N + 1) −1] (X1 / R)
+ [1- {n (N + 1) -1} (Σ / R)] n1 · θ1
(Equation 40) Σ = R / [n (N + 1) −1]
(Equation 41) (nu) = [n (N + 1) -1] (X1 / R)
Here, Σ is given by (Equation 42).
(Expression 42) Σ = d1 / n1 + d2 / n2 +... + D (N + 1) / n (N + 1)

  FIG. 3 shows the case where the transparent plate 401 has one layer in FIG. 4 (N = 1), and (Equation 39) through (Equation 41) become (Equation 29) through (Equation 31). In this case, d1 = S, d (N + 1) = d2 = H, and X1 = δ.

Any lenticular lens must satisfy at least the paraxial approximation. The refractive index and thickness of each transparent plate and cylindrical lens portion must satisfy (Equation 30) or (Equation 40).
(Embodiment 1)

In the first embodiment, the lens shape is a spherical surface. In FIG. 3, the distance from the lens center line 304 of the point P2 is X, and the lens shape is represented by (Equation 1). This (Expression 1) represents an ellipse, and m is called an elliptic coefficient. A spherical surface is a special case of an ellipse, where m = 1. In this lens shape, the radius of curvature at the center of the lens is R.
(Expression 1) F (X) = T−mR + [(mR) ² −mX ² ] ^1/2

  In the case of a spherical surface, simulation is performed using (Equation 1) and (Equation 16) to (Equation 21). If (Equation 1) is used, the equation (Equation 19) becomes a quadratic equation of X, and a solution can be obtained algebraically. For example, in FIG. 3, m = 1, R = 1, T = 2.338, S = 2.0, n1 = 1.5, n2 = 1.65, and W = 1.5. These conditions satisfy (Equation 30). FIG. 5 shows the result of the simulation. The horizontal axis represents the position (X1) where light emitted from a point on the image plane enters the boundary surface, and the vertical axis represents the emission angle (ν) from the cylindrical lens. As the points on the image plane (distance δ from the lens center line), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light emitted from a point on the image plane corresponding to the adjacent spherical cylindrical lens.

The result of FIG. 5 shows that the viewing angle can be expanded to ± 0.4 radians (± 23 degrees) by increasing the refractive index of only the cylindrical lens portion without increasing the width W of the cylindrical lens. Yes. Further, since the high refractive index resin is used only for the cylindrical lens portion, the decrease in transmittance is also reduced. The thickness of the high refractive index resin is H = 0.34.
(Embodiment 2)

  In order to reduce the thickness of the high refractive index resin and to enlarge the viewing angle, an aspherical cylindrical lens is used. FIG. 6 is a diagram for explaining the shape of an aspheric cylindrical lens.

  In FIG. 6, reference numeral 601 (dashed line) denotes a spherical lens shape, and 602 (solid line) denotes an aspheric lens shape. Reference numeral 603 denotes an image plane, and reference numeral 604 denotes a lens center line. Near the lens center line 604, paraxial approximation needs to be satisfied, and the shape 602 can approximate a spherical surface. FIG. 6 shows a case where the radius of curvature at the lens center line of the spherical lens 601 and the aspherical lens 602 is the same, the center of the curved surface is O1, and the radius of curvature is an interval R1 between Q1 and O1. As the distance from the lens center line 604 increases, the gradient of the lens shape 602 becomes smaller than the gradient of the spherical lens shape 601. That is, the radius of curvature of the lens shape increases as the distance from the lens center line 604 increases. The center of the curved surface near the point Q2 is O2, and the radius of curvature is an interval R2 between Q2 and O2. The center of the curved surface near the point Q3 is O3, and the radius of curvature is an interval R3 between Q3 and O3. The curvature radius R2 near the point O2 is larger than the curvature radius R1 near the point O1, and the curvature radius R3 near the point O3 is larger than the curvature radius R2 near the point O2.

  Examples of aspheric shapes include ellipses and hyperbolic curves. The curvature of the hyperbola is more gradual than the ellipse. Alternatively, there is a quaternary even function having an intermediate shape between an ellipse and a hyperbola, and a combination of an ellipse, a hyperbola, or a quartic even function can be considered.

  In the second embodiment, the lens shape is approximately an ellipse. In the case of an ellipse, simulation is performed using (Equation 1) and (Equation 16) to (Equation 21). If (Equation 1) is used, the equation (Equation 19) becomes a quadratic equation of X, and a solution can be obtained algebraically. As an example, in FIG. 3, m = 3, R = 1, T = 2.335, S = 2.039, n1 = 1.5, n2 = 1.65, and W = 1.5. These conditions satisfy (Equation 30). FIG. 7 shows the result of the simulation. The horizontal axis represents the position (X1) where light emitted from a point on the image plane enters the boundary surface, and the vertical axis represents the emission angle (ν) from the elliptical cylindrical lens. As a point on the image plane (distance δ from the lens center line 304), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light emitted from a point on the image plane corresponding to the adjacent elliptic cylindrical lens.

The result of FIG. 7 shows that the viewing angle can be expanded to ± 0.46 radians (± 26 degrees) by increasing the refractive index of only the cylindrical lens portion without increasing the width W of the cylindrical lens. Yes. Further, since the high refractive index resin is used only for the cylindrical lens portion, the decrease in transmittance is also reduced. The thickness of the high refractive index resin is H = 0.30, which can be made thinner than the spherical surface.
(Embodiment 3)

In order to further reduce the thickness of the high-refractive-index cylindrical lens portion, in Embodiment 3, the lens shape is approximately a hyperbola. In FIG. 3, a lens shape that can be approximated by a hyperbola is represented by (Equation 43). Here, m is referred to as a hyperbola coefficient that determines the shape of the hyperbola. In this lens shape, the radius of curvature at the center of the lens is R.
(Formula 43) F (X) = T + mR − [(mR) ² + mX ² ] ^1/2

  In the case of a hyperbola, simulation is performed using (Equation 43) and (Equation 16) to (Equation 21). Using (Equation 43), the equation (Equation 19) becomes a quadratic equation of X, and a solution can be obtained algebraically. As an example, in FIG. 3, m = 3, R = 1, T = 2.332, S = 2.06, n1 = 1.5, n2 = 1.65, and W = 1.5. These conditions satisfy (Equation 30). FIG. 8 shows the result of the simulation. The horizontal axis represents the position (X1) where light from a point on the image plane enters the boundary surface, and the vertical axis represents the emission angle (ν) from the hyperbolic cylindrical lens. As the points on the image plane (distance δ from the lens center line), five cases of 0, W / 4, W / 2, 3W / 4, and W are shown. δ = 3W / 4 and δ = W are light from points on the image plane corresponding to adjacent hyperbolic cylindrical lenses.

The result of FIG. 8 shows that the viewing angle becomes ± 0.46 radians (± 26 degrees) if the refractive index of only the lens portion is increased without increasing the width W of the hyperbolic cylindrical lens. . Further, since the high refractive index resin is used only for the cylindrical lens portion, the decrease in transmittance is also reduced. The thickness of the high refractive index resin is H = 0.27 and can be made thinner than an ellipse.
(Embodiment 4)

In the second embodiment, the lens shape is an ellipse, and in the third embodiment, the lens shape is a hyperbola. In the fourth embodiment, a fourth-order even function having a lens shape intermediate between an ellipse and a hyperbola is selected, and F (X) representing the lens shape is expressed by (Equation 44). Here, (ρW) is the X coordinate of the inflection point of the fourth order even function. Using (Equation 44), the equation (Equation 19) becomes a quaternary equation of X, and a solution can be obtained algebraically using the Ferrari solution. Although details are not shown here, the result is intermediate between FIGS.
(Equation 44) F (X) =-[1 / {12R (ρW) ² }] · X ⁴
+ [1 / (2R)] · X ²
(Embodiment 5)

Up to now, spherical, elliptical, hyperbolic, and fourth-order even numbers have been shown as lens shapes. A lens shape combining these can also be selected. For example, an example in which an ellipse and a hyperbola are combined is expressed by (Equation 45) as an average of (Equation 1) and (Equation 43). Other combinations may also be used.
(Equation 45) F (X) = T + [{(mR) ² −mX ² } ^1/2 − {(mR) ² + mX ² } ^1/2
(Embodiment 6)

  In the first to third embodiments of the present invention, the radius of curvature R = 1 near the lens center line has been described using a relative size. In the sixth embodiment of the present invention, a more specific example is shown based on the third embodiment of the present invention. The lens shape is a hyperbola.

  A 60 LPI (60 lenses per inch) lenticular lens is used, and the width (W) of the cylindrical lens is 0.42 mm. In Embodiment 3 of the present invention, W = 1.5, which corresponds to 0.42 mm. Accordingly, the radius of curvature (R) in the vicinity of the lens center line is 0.28 mm. The distance from the image plane to the top of the hyperbolic cylindrical lens (T = 2.332) and the distance from the image plane to the boundary between the transparent plate and the lens section (S = 2.005) are T = 0.66 mm, S = 0.58 mm. The transparent plate is made of a general resin (refractive index 1.5), and the lens part is made of a nanocomposite resin having a refractive index of 1.65 in which zirconium oxide is dispersed in an ultraviolet curable resin.

FIG. 9 is a cross-sectional view of the lenticular lens of the above specific example. In FIG. 9, 901 is a transparent plate made of a general resin, 902 is a hyperbolic cylindrical lens portion made of a nanocomposite resin having a high refractive index, 903 is an image plane, 904 is a center line of the hyperbolic cylindrical lens, and 905 is a transparent plate 901. And the cylindrical lens portion 902. The entire thickness of the lenticular lens is 0.66 mm, and the high refractive index nanocomposite resin is 0.08 mm even at the thickest part, so that sufficient transparency can be secured.
(Embodiment 7)

  Next, the first stereoscopic image display method of the present invention will be described. A multi-viewpoint image is displayed on the image plane. Adjacent images on the image plane corresponding to one cylindrical lens have a strong correlation with each other, and even if mixed, it does not pose a big problem for image quality degradation. However, the image near the boundary between adjacent cylindrical lenses has a low correlation, and when they are mixed, the image quality deteriorates. When displaying a stereoscopic image, if an image is not displayed near the boundary between adjacent cylindrical lenses, it is possible to prevent images having low correlation from being mixed.

  A seventh embodiment of the present invention will be described with reference to FIG. In FIG. 10, 1001 is a transparent plate, 1002 is a cylindrical lens portion made of a high refractive index resin, 1003 is an image plane, 1004 is a center line of the cylindrical lens, and 1005 is a boundary between the transparent plate 1001 and the cylindrical lens portion 1002. . Reference numeral 1006 denotes a displayed image. The image is displayed only in about 80% of the image plane 1003, and no image is displayed near the boundary between adjacent cylindrical lenses. FIG. 10 shows an example of about 80%, but the example is not limited.

Embodiment 7 of the present invention is also effective for a conventional lenticular lens. FIG. 11 shows an example in which Embodiment 7 of the present invention is applied to a conventional lenticular lens. In FIG. 11, reference numeral 1101 denotes a lenticular lens, 1102 denotes an image plane, and 1103 denotes a displayed image.
(Embodiment 8)

  The second stereoscopic image display method of the present invention will be described. FIG. 12 is a diagram illustrating the relationship between the eye position and light rays when viewing a stereoscopic image. In FIG. 12, reference numeral 1201 denotes a transparent plate, 1202 denotes a lens portion made of a high refractive index resin, and 1203 denotes an image plane. In general, viewing from the center of the lenticular lens, 1204 is the position of the eye. FIG. 12 shows only the center, left end, and right end of the lenticular lens, 1205 is an image at the center, 1206 is an image at the left end, and 1207 is an image at the right end. With the eyes 1204, an image near the lens center line is viewed at the center, an image on the left side of the lens center line is viewed at the left end, and an image on the right side of the lens center line is viewed at the right end. Therefore, if the eye position is moved a little, there is a high possibility that the images on the left and right edges will deviate from the viewing angle.

  Therefore, an image is displayed centering on the outer peripheral side of the cylindrical lens center line from the center of the lenticular lens to the outer peripheral side. This is shown in FIG. In FIG. 13, the same components as those in FIG. 1208 is the position of the leftmost image, and 1209 is the position of the rightmost image. All of the central portion 1205, the left end 1208, and the right end 1209 are such that light rays from the central portion of the image are incident on the eye, and even if the eye position moves a little, it does not deviate from the viewing angle.

Embodiment 8 of the present invention is also effective for a conventional lenticular lens. FIG. 14 shows an example in which Embodiment 8 of the present invention is applied to a conventional lenticular lens. In FIG. 14, 1401 is a lenticular lens, 1402 is an image plane, 1403 is an eye, 1404, 1405, and 1406 are displayed images.
(Embodiment 9)

In Embodiment 9 of the present invention, a nanocomposite resin having a refractive index n2 = 1.75 is synthesized by increasing the mixing ratio of fine particles in order to increase the viewing angle a little. A hyperbolic cylindrical lens is used, and in FIG. 3, m = 3, R = 1, T = 2.04, S = 1.77, n1 = 1.5, n2 = 1.75, and W = 1.5. FIG. 15 shows the result of simulation using (Equation 43) and (Equation 16) to (Equation 21). The viewing angle expands to ± 0.52 radians (± 30 degrees). It can also be seen that since the refractive index of the cylindrical lens portion is made higher, the distance (T) between the lens top and the image plane becomes smaller.
(Embodiment 10)

Next, Embodiment 10 of the present invention shows a method for increasing the viewing angle at the expense of some resolution. Using a nanocomposite resin with a refractive index n2 = 1.75, the hyperbolic lenticular lens width is increased to W = 1.7. In FIG. 3, it is assumed that m = 3, R = 1, T = 2.05, S = 1.71, n1 = 1.5, n2 = 1.75, and W = 1.7. FIG. 16 shows the result of simulation using (Equation 43) and (Equation 16) to (Equation 21). It can be seen that the viewing angle expands to ± 0.57 radians (± 33 degrees).
(Embodiment 11)

  In Embodiments 1 to 10 of the present invention, the erecting lenticular lens has been described, but it can also be used for an inverted lenticular lens as in the conventional example. FIG. 17 shows an inverted lenticular lens in which only the cylindrical lens portion is made of a nanocomposite resin having a high refractive index.

In FIG. 17, 1701 is a transparent plate made of a general resin, 1702 is a cylindrical lens portion made of a nanocomposite resin having a high refractive index, and 1703 is an image plane. Even when an inverted lenticular lens is used, it is possible to obtain a lenticular lens having a large viewing angle, a high resolution, a low manufacturing cost, and being difficult to break.
Embodiment 12

  When displaying a stereoscopic image, it is inevitable that the resolution is lower than that of a planar image. It becomes difficult to interpret small letters. However, when displaying a stereoscopic image, it is desirable to display small characters in the explanation of the display contents. Therefore, a part of the image display device does not have a lenticular lens and is provided with a part that always displays a planar image. In other parts, the lenticular lens according to any one of Embodiments 1 to 11 of the present invention is provided to display a stereoscopic image.

FIG. 18 shows an example in which a portion that always displays a planar image is installed at the bottom of the screen. In FIG. 18, 1801 is an image display device, 1802 is a lenticular lens that displays a stereoscopic image, and 1803 is a portion that always displays a flat image. In 1803, an explanatory character of the display content is displayed. Embodiment 12 of the present invention is also effective for a conventional lenticular lens. In FIG. 18, the planar image display unit 1803 is arranged at the bottom, but it may be at the left or right edge or the top.
(Embodiment 13)

  In the first to twelfth embodiments of the present invention, the cylindrical lens is used as the lens. However, the same can be achieved by using a fly-eye lens in which single lenses are arranged in a matrix in the vertical and horizontal directions. Such a fly eye lens is shown in FIG. In FIG. 19, 1901 is a single convex lens, and 1902 is an array of single convex lenses, that is, a fly's eye lens. If a fly's eye lens is used, the left and right eyes can recognize a stereoscopic image even if the image apparatus is rotated 90 degrees.

In Embodiments 1 to 13 of the present invention, a lenticular lens in which an array of high refractive index cylindrical lenses or an array of single lenses is formed on a transparent plate is used. A method for manufacturing such a lenticular lens will be described.
(Embodiment 14)

  A first manufacturing method of the lenticular lenses according to the first to thirteenth embodiments of the present invention will be described with reference to FIG. In FIG. 20, 2001 is a transparent plate made of a general resin, 2002 is a mold having a lens array, 2003 is a first high-refractive index UV curable resin, 2004 is an UV lamp, and 2005 is UV. The transparent plate 2001 and the mold 2002 are made to face each other, a first ultraviolet curable resin 2003 having a high refractive index is inserted between them, and ultraviolet rays 2005 are irradiated from the transparent plate 2001 side to thereby provide a first ultraviolet ray having a high refractive index. The cured resin 2003 is cured. A lenticular lens having a lens portion made of a high refractive index resin is formed.

As the first ultraviolet curable resin 2003 having a high refractive index, a nanocomposite resin in which fine particles having a high refractive index are dispersed in a general ultraviolet curable resin (base material) can be used. As the high refractive index fine particles, dielectric fine particles such as titanium oxide, zirconium oxide, zinc oxide or aluminum oxide having a diameter of 10 nanometers or less are used.
(Embodiment 15)

  A second method for manufacturing the lenticular lens according to the first to thirteenth embodiments of the present invention will be described with reference to FIG. In FIG. 21, the same components as those in FIG. 20 are denoted by the same reference numerals and description thereof is omitted. Reference numeral 2006 denotes a second ultraviolet curable resin layer. (A) A second ultraviolet curable resin layer 2006 is formed on the transparent plate 2001. (B) The second ultraviolet curable resin layer 2006 and the mold 2002 are opposed to each other, the first ultraviolet curable resin 2003 having a high refractive index is inserted between them, and ultraviolet rays 2005 are irradiated from the transparent plate 2001 side. The first and second UV curable resins are cured simultaneously. (C) As a result, a lenticular lens having a lens portion made of a high refractive index resin is formed.

  As the first ultraviolet curable resin 2003 having a high refractive index, a nanocomposite resin in which fine particles having a high refractive index are dispersed in an ultraviolet curable resin (base material) can be used as in the case of the fourteenth embodiment. In order to increase the refractive index of the nanocomposite resin, it is necessary to increase the amount of fine particles dispersed in the ultraviolet curable resin, and therefore the degree of curing by ultraviolet rays decreases. In the fourteenth embodiment (FIG. 20), the adhesion between the general resin transparent plate 2001 and the nanocomposite resin 2003 constituting the convex lens portion may be reduced and peeled off.

  As the second ultraviolet curable resin layer 2006, an ultraviolet curable resin that does not contain fine particles having a high refractive index or an ultraviolet curable resin having a small amount of dispersion of fine particles having a high refractive index is used. This second ultraviolet curable resin has a high degree of curing by ultraviolet rays and has high adhesion to the transparent plate 2001. In addition, since the first ultraviolet curable resin 2003 and the second ultraviolet curable resin 2006 are cured at the same time, the first ultraviolet curable resin 2003 and the second ultraviolet curable resin 2006 are mixed at the boundary and the adhesion is increased. Accordingly, a stable lenticular lens having a high refractive index lens array can be obtained.

  If the base material of the first ultraviolet curable resin 2003 is used as the second ultraviolet curable resin 2006, the affinity between the first and second ultraviolet curable resins is higher and the adhesion is higher.

  The refractive index of the second ultraviolet curable resin 2006 will be described. The refractive index of an ultraviolet curable resin that does not contain fine particles with a high refractive index is about the same as the refractive index of a general resin, and is about the same as the refractive index (n1) of the transparent plate 2001. In addition, an ultraviolet curable resin with a small amount of dispersion of high refractive index fine particles has a higher refractive index than the ultraviolet curable resin as a base material, but has a lower refractive index than the nanocomposite resin 2003 of the lens array portion, It has a refractive index between the refractive index (n1) of the transparent plate 2001 and the refractive index (n2) of the nanocomposite resin 2003. Therefore, if the thickness of the resin layer 2006 is appropriately selected, an antireflection effect between the transparent plate 2001 and the nanocomposite resin 2003 can also be produced.

  In general, the thickness of the resin layer 2006 is very thin compared to the thickness of the transparent plate 2001 and the nanocomposite resin 2003. Therefore, as can be seen from (Equation 40) and (Equation 42), the thickness of the resin layer 2006 has little influence on the lenticular lens effect.

As a method of forming the second ultraviolet curable resin layer 2006 on the transparent plate 2001, a spinn coating method in which a resin solution before curing is applied while rotating the transparent plate, or a roller to which a resin solution before curing is attached. It is possible to use a method in which the resin is applied by rotating the substrate on a transparent plate.
(Embodiment 16)

  A third method of manufacturing the lenticular lens according to the first to thirteenth embodiments of the present invention will be described with reference to FIG. In FIG. 22, 2201 is a resin sheet, 2202 is a mold having a lens array, 2203 is a transparent plate made of a general resin, 2204 is a third UV curable resin layer, 2205 is an UV lamp, and 2206 is UV. . (A) The mold 2202 is pressed against the resin sheet 2201 to form a lens array on one surface of the resin sheet 2201. (B) A third ultraviolet curable resin layer 2204 is formed on the transparent plate 2203, and a resin sheet 2201 on which a lens array is formed is overlaid thereon. (C) The third ultraviolet curable resin 2204 is cured by irradiating with ultraviolet rays 2206, and a lenticular lens having a lens portion made of a high refractive index resin can be obtained.

  As a material of the resin sheet 2201, a nanocomposite resin in which fine particles having a high refractive index are dispersed in an ultraviolet curable resin (base material) can be used. As the high refractive index fine particles, dielectric fine particles such as titanium oxide, zirconium oxide, zinc oxide or aluminum oxide having a diameter of 10 nanometers or less are used.

  The first method for forming a lens array on one side of the resin sheet 2201 is to cure the resin sheet made of nanocomposite resin by irradiating with ultraviolet rays, and then press the mold 2202 to form the lens array.

  The second method of forming a lens array on one side of the resin sheet 2201 is to irradiate the resin sheet made of nanocomposite resin with weak ultraviolet rays so that the resin sheet is not completely cured. Then, the mold 2202 is pressed to form a lens array.

As the third ultraviolet curable resin 2204, the same material as that of the second ultraviolet curable resin 2006 of Embodiment 15 (FIG. 21) can be used. If a lens array is formed on the above-mentioned semi-cured resin sheet, and then the third UV curable resin 2204 and the semi-cured resin sheet 2201 are simultaneously cured with UV light 2206, the third UV curable resin 2204 and The base material of the resin sheet 2201 is mixed slightly and the adhesion becomes high. Further, the refractive index of the third ultraviolet curable resin 2204 has the same value as that of the second ultraviolet curable resin of the fifteenth embodiment.
(Embodiment 17)

  A third method for forming a lens array on one side of a resin sheet will be described with reference to FIG. In FIG. 23, 2301 is a resin sheet, and 2302 is a roller having a lens array mold formed on its surface. The roller 2302 is rotated while being pressed against the resin sheet 2301 to form a lens array on one surface of the resin sheet 2301. The resin sheet on which this lens array is formed can be used in the same manner as the resin sheet 2201 of the sixteenth embodiment.

  The first to seventeenth embodiments disclosed above are merely examples of the present invention, and the present invention is not construed as being limited by these embodiments. The scope of the present invention is shown not by the above embodiment but by the scope of claims, and is intended to include all modifications within the meaning and scope equivalent to the scope of claims.

  The lenticular lens of the present invention can provide a stereoscopic image with a large viewing angle and a high resolution, is low in manufacturing cost, is difficult to break, and is safe. Therefore, the present invention can be applied to uses such as a stereoscopic television, a portable device, a personal computer monitor, a game machine, a stereoscopic picture book, and a stereoscopic photograph.

  The method for producing a lenticular lens of the present invention can provide a method for forming a lens portion having a high refractive index on a transparent plate. Accordingly, the present invention can be applied to the production of lenticular lenses used for stereoscopic televisions, portable devices, personal computer monitors, game machines, stereoscopic picture books, stereoscopic photographs, and the like.

In addition, the lenticular lens in which the high refractive index lens portion is formed on the transparent plate is not limited to a stereoscopic image, and can be used for various purposes in the future.

Claims (1)

A transparent plate is installed on the image plane, a convex cylindrical lens portion is formed in an array on the opposite side of the transparent plate from the image plane, the refractive index of the transparent plate is n1, and the refractive index of the convex cylindrical lens portion is Where the ratio is n2, the distance from the image plane to the top of the convex cylindrical lens is T, the radius of curvature of the convex cylindrical lens near the lens center line passing through the top of the convex cylindrical lens is R, the distance from the lens center line Is X, the convex cylindrical lens shape is an elliptic curve, T + 3R − [(3R) ² + 3X ^2, the distance from the image plane being represented by T-3R + [(3R) ² −3X ² ] ^1/2. ] hyperbola represented by ^1/2, or expressed in an intermediate shape between the elliptic curve and the hyperbola, and is characterized in that it is n2> n1 Renchikyu Renzu.

Images