JP5272271B2 - Image display - Google Patents

Description

  The present invention relates to a stereoscopic image display object. In particular, the present invention relates to a stereoscopic image display device and a stereoscopic image printed matter.

  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. 28 is a perspective view of a lenticular lens. In FIG. 28, reference numeral 2801 denotes a plurality of cylindrical lenses arranged in parallel.

  FIG. 29 is a cross-sectional view of a stereoscopic image display apparatus using a lenticular lens. In FIG. 29, reference numeral 2901 denotes a lenticular lens, 2902 denotes an image display unit, and 2903 denotes a transparent panel for protecting the image display unit. Examples of the image display portion 2902 include a liquid crystal layer, a plasma discharge portion, and an organic EL layer. FIG. 29 shows a structure in which a lenticular lens 2901 is bonded to a general display including an image display unit 2902 and a transparent panel 2903. A multi-viewpoint image is displayed on the image display unit 2902, and the image is stereoscopically recognized by being viewed with the left and right eyes through the lenticular lens 2901. If both the lenticular lens 2901 and the transparent panel 2903 are made of general glass or resin, their refractive indexes are comparable. In that case, the lenticular lens 2901 and the transparent panel 2903 are optically handled integrally.

  One method for capturing a multi-viewpoint image is to capture an image of the subject from many directions. FIG. 30 is a configuration diagram for capturing a multi-viewpoint image. FIG. 30 shows an example in which five cameras are used. In FIG. 30, a subject 3001 is imaged using five cameras 3002 to 3006. The plurality of captured images have parallax with each other.

  FIG. 31 is a diagram showing a method for creating a multi-viewpoint image. In FIG. 31, reference numerals 3102 to 3106 denote images taken by the cameras 3002 to 3006 in FIG. These captured images are divided into strip images and combined into one as shown in FIG. 31 to obtain a multi-viewpoint image 3101. In the example of five viewpoints as shown in FIGS. 30 and 31, the images are synthesized into 3101 using the corresponding one-fifth portion of each strip image. 3101 shows only a multi-viewpoint image corresponding to one cylindrical lens. In practice, multi-viewpoint images corresponding to all cylindrical lenses are created.

  32 and 33 are diagrams showing the principle of stereoscopic viewing using a lenticular lens. 32 and 33, 3201 is a cylindrical lens, 3202 is an image display surface. In FIGS. 32 and 33, the lenticular lens (2901 in FIG. 29) and the transparent panel (2903 in FIG. 29) are handled as one body. An image 3203 displayed on the image display surface 3202 is a portion corresponding to one cylindrical lens of the multi-viewpoint image 3101 in FIG. In the example of FIGS. 32 and 33, the multi-viewpoint image 3203 is shown only on the image display surface corresponding to one cylindrical lens. Actually, a multi-viewpoint image is displayed on an image display surface corresponding to all cylindrical lenses. The light emitted from each point on the image display surface becomes substantially parallel light by the cylindrical lens and enters the right eye or the left eye. In the positions of the right eye 3204 and the left eye 3205 as shown in FIG. 32, the substantially blind light 3206 is incident on the right eye 3204, the substantially parallel light 3207 is incident on the left eye 3205, and the right eye and the left eye are mutually connected. A stereoscopic image is recognized by looking at an image with parallax.

  Further, when the positions of the right eye 3204 and the left eye 3205 are changed as shown in FIG. 33 by moving the head position, the substantially parallel light 3208 is incident on the right eye 3204 and the substantially parallel light is incident on the left eye 3205. Light 3209 is incident to recognize the image three-dimensionally. Moving the head changes the three-dimensional direction, and things that were not visible in FIG. 32 become visible in FIG. 33, increasing the sense of reality.

  In the lenticular lenses as shown in FIGS. 32 and 33, the light emitted from different points on the image display surface 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. The substantially parallel light in the specification of the present invention includes completely parallel light, light that tends to converge slightly, and light that tends to spread slightly.

  In FIG. 34, 3401 is a cylindrical lens, and 3402 is an image display surface. Also in FIG. 34, the lenticular lens (2901 in FIG. 29) and the transparent panel (2903 in FIG. 29) are handled as a unit. In FIG. 34, a spherical lens is used, and the spherical radius of the lens is R. Let T be the distance from the image display surface 3402 to the top of the lens, n be the refractive index of the lens medium, and W be the width of one cylindrical lens. Let δ be the distance from the lens center line 3403 passing through the top of the lens to the point of interest on the image display surface. The light coming out from the point on the image display surface and reaching the point P on the lens surface is refracted on the lens surface and emitted from the cylindrical lens 3401 with an angle β.

The distance X of the point P from the lens center line 3403 is expressed by (Equation 1), and the angle θ of the light ray from the point of interest on the image display surface toward the point P is obtained by (Equation 2). Further, the incident angle α to the lens surface is obtained by (Equation 3), and the emission angle β is obtained by (Equation 4) from the law of refraction on the lens surface.
(Equation 1) X = R · sinφ
(Formula 2) tan θ = (δ−X) / (T−R + R · cos φ)
(Equation 3) α = θ + φ
(Expression 4) sin (φ + β) = n · sin α

  If a point on the image display surface (distance δ from the lens center line 3403) and a refraction point P (distance X from the lens center line 3403) are given, then φ, θ, α, and β are obtained, and the direction of light emitted from the cylindrical lens 3401 is obtained.

  Ideally, light emitted from different points on the image display surface 3402 is emitted as parallel light having different emission angles from the cylindrical lens 3401. FIG. 35 shows the ideal behavior. The horizontal axis represents the position (X) where light emitted from a point on the image display surface enters the lens surface, and the vertical axis represents the emission angle (β) from the cylindrical lens. The five cases of 0, W / 4, W / 2, 3W / 4, and W are shown as points on the image display surface (distance δ from the lens center line 3403). δ = 3W / 4 and δ = W are light emitted from a point on the image display surface corresponding to the adjacent cylindrical lens. For example, light emitted from a point (δ = W / 4) on the image display surface 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 display surface becomes parallel light with a constant emission angle regardless of the incident position of 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 4) are expressed as (Equation 5) to (Equation 8), respectively.
(Equation 5) X = Rφ
(Equation 6) θ = (δ−X) / T
(Equation 7) α = θ + φ
(Equation 8) φ + β = nα

From these (Equation 5) to (Equation 8), the exit angle β in paraxial approximation is expressed by (Equation 9). The condition that the lenticular lens effect, that is, the light emitted from a point on the image display surface (distance δ from the lens center line 3403) becomes substantially parallel light with a constant emission angle is that β does not depend on θ, ). The emission angle β at that time is given by (Equation 11). When T is given by (Equation 10), the light emitted from the image display surface becomes parallel light, and therefore T corresponds to the focal length of the spherical lens having the radius R.
(Equation 9) β = (n−1) (δ / R) − [(n−1) (T / R) −n] θ
(Equation 10) T = Rn / (n-1)
(Equation 11) 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 display surface to the top of the cylindrical lens is (Equation 12), and the emission angle β of substantially parallel light is (Equation 13) This means that the focal length of a spherical lens made of a medium having a refractive index of about 1.5 is three times the spherical radius.
(Equation 12) T = 3R
(Equation 13) β = δ / (2R)

  Next, a general case is simulated using (Equation 1) to (Equation 4). As an example, in FIG. 34, R = 1, T = 3, n = 1.5, and W = 1.5. These conditions satisfy (Equation 10). FIG. 36 shows the result of the simulation. The horizontal axis represents the position (X) where light emitted from a point on the image display surface enters the lens surface, and the vertical axis represents the exit angle (β) emitted from the cylindrical lens. The five cases of 0, W / 4, W / 2, 3W / 4, and W are shown as points on the image display surface (distance δ from the lens center line 3403). δ = 3W / 4 and δ = W are light emitted from a point on the image display surface corresponding to the adjacent cylindrical lens.

  The following can be understood from FIG. Most of the light emitted from the lens center (δ = 0) of the image display surface is emitted from the cylindrical lens as substantially parallel light having an angle β = 0, and the light in the peripheral portion becomes slightly focused light. This degree of focused light does not disturb the lenticular effect. When the light emitted from the point (δ = W / 4) on the image display surface at a distance W / 4 from the lens center line is incident on the lens surface range (−0.75 to +0.5), the angle β = 0. When it is emitted from the cylindrical lens as substantially parallel light having .19 radians and enters the range (+0.5 to +0.75) of the lens surface, it becomes non-parallel light. In addition, when the light emitted from the point (δ = W / 2) on the image display surface 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 lens surface range (+0.3 to +0.6), 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. 35 and FIG. 36, a lot of light is relatively close to the ideal, but there is also light that is out of the ideal. The effect on the image of rays that deviate from this ideal must be considered.

  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, that is, if crosstalk is large, a plurality of images are mixed and 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. 37, the same components as those of FIG. Reference numeral 3404 denotes an eye having an angle of 0.19 radians. In FIG. 37, the eye 3404 is drawn so as to be close to the lenticular lens, but it is actually far in the direction of the arrow. As can be seen from FIG. 36, most of the light emitted from the point (δ = W / 4) on the image display surface is substantially parallel light having an emission angle of 0.19 radians. These are lights in a region surrounded by the light beam 3405 (solid line) and the light beam 3406 (solid line) in FIG. 37, and this substantially parallel light can be seen from the eye 3404. Light such as a light ray 3407 (wave line) emitted from a point (δ = W / 4) on the image display surface has an emission angle larger than 0.19 radians and cannot be seen from the eye 3404.

  Next, the case where the lenticular lens is viewed from an angle of 0.37 radians will be described with reference to FIG. In FIG. 38, the same components as those in FIGS. 34 and 37 are denoted by the same reference numerals and description thereof is omitted. The eye 3404 is at a distance of 0.37 radians (in the direction of the arrow). As can be seen from FIG. 36, most of the light emitted from the point (δ = W / 2) on the image display surface becomes substantially parallel light having an emission angle of 0.37 radians. These are lights in a region surrounded by the light beam 3408 (solid line) and the light beam 3409 (solid line) in FIG. 38, and this substantially parallel light can be seen from the eye 3404. On the other hand, part of light from other points on the image display surface also has an emission angle of 0.37 radians. For example, light ray 3410 (dashed line) exits from a point where δ = W / 4 and is emitted with an exit angle of 0.37 radians. The light beam 3410 is generated in a very narrow range as compared with the area surrounded by the light beams 3408 and 3409, and the light amount 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. 36, 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 3407 (dashed line) in FIG. Further, as seen from a light ray 3410 (dashed line) in FIG. 38, the amount of light is small when viewed from a specific emission angle, and there is no problem in degradation of image quality.

  Images from many viewpoints are displayed on the image display surface corresponding to one cylindrical lens. Of these multi-viewpoint images, the adjacent images are images taken by the adjacent cameras in FIG. 30 and have a strong correlation with each other. However, the image near the boundary between adjacent cylindrical lenses is, for example, an image captured by the cameras 3002 and 3006 in FIG. 30, and the correlation is low. When they are mixed, the image quality deteriorates.

  Accordingly, the light exiting from the boundary point (δ = W / 2) between adjacent cylindrical lenses and emitted from the cylindrical lens has a relatively high intensity (the gradient of the curve representing the exit angle is small) and the smallest. The emission angle determines the viewing angle of the stereoscopic image. The viewing angle in the case of FIG. 36 is ± 0.37 radians (± 21 degrees). The larger the viewing angle, the better the stereoscopic image can be viewed even if the head position is moved a little, and a stable stereoscopic image can be obtained.

  As shown in FIG. 36, most of the light (δ> W / 2) emitted from the image display surface corresponding to the adjacent cylindrical lens is also substantially parallel light, but the point on the image display surface is closer to the lens center line. As the distance increases, 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. However, it represents that a stereoscopic image can be viewed outside the viewing angle as in the viewing angle, and this is called a side lobe.

Although the spherical lens is used in FIG. 34, an elliptical lens has been proposed to improve the image quality (see, for example, Patent Document 1). In the case of FIG. 34, since the distance from the image display surface 3402 to the top of the cylindrical lens 3401 is T, the elliptical lens is represented by (Expression 14). Patent Document 1 proposes an elliptic lens with the condition of (Equation 15). Here, R is the radius of curvature near the center of the lens, and n is the refractive index of the lens medium. The lens medium is glass or resin and generally has a refractive index greater than 1.4. Therefore, k is larger than 0.5 by (Equation 15).
(Equation 14) Y = T−X ² / [R + (R ² −kX ² ) ^1/2 ]
(Expression 15) k = 1− (1 / n) ²

  As described above, a stereoscopic image can be recognized using a lenticular lens. However, if the planar image is viewed through the lenticular lens, only a part of the planar image corresponding to the viewing direction is viewed, and the resolution deteriorates. In particular, small characters may become unreadable. Thus, an image display device that can switch between a planar image and a stereoscopic image has been proposed (see, for example, Patent Document 2 and Patent Document 3).

  FIG. 39 is a cross-sectional view of the image display device described in Patent Document 2. In FIG. 39, 3901 is an array of one-convex cylindrical lenses, 3902 is an image display unit, and 3903 is a transparent panel that protects the image display unit. The array 3901 of single convex cylindrical lenses is made of a material whose refractive index changes electrically. When the refractive index of the single-convex cylindrical lens 3901 is high, a multi-viewpoint image is displayed on the image display unit 3902, and the array of single-convex cylindrical lenses acts as a lenticular lens and can recognize a stereoscopic image. When the refractive index of the single-convex cylindrical lens 3901 is low and the same as that of the surrounding medium, a planar image is displayed on the image display unit 3902, and the array of the single-convex cylindrical lenses functions as a simple transparent plate and can recognize the planar image. Liquid crystal can be used as a substance whose refractive index changes electrically.

FIG. 40 is a cross-sectional view of the image display device described in Patent Document 3. In FIG. 40, 4001 is an array of biconvex cylindrical lenses, 4002 is an image display unit, and 4003 is a transparent panel that protects the image display unit. The array 4001 of biconvex cylindrical lenses is made of a material whose refractive index changes electrically or a material having anisotropy with respect to the polarization of light. For example, when a material whose refractive index is electrically changed is used, if the refractive index of the biconvex cylindrical lens 4001 is high, a multi-viewpoint image is displayed on the image display unit 4002, and the array of biconvex cylindrical lenses is used as a lenticular lens. A working stereo image can be recognized. In addition, when the refractive index of the biconvex cylindrical lens 4001 is low and about the same as the surrounding medium, a planar image is displayed on the image display unit 4002, and the array of biconvex cylindrical lenses acts as a mere transparent plate to recognize the planar image. it can. Liquid crystal can be used as a substance whose refractive index changes electrically.
JP-A-8-286148 Special Table 2000-503424 JP 2006-276466 A

  In Patent Document 2, since a single convex cylindrical lens is used, the refraction angle is small and the viewing angle is also small. In patent document 3, since a biconvex cylindrical lens is used, a refraction angle becomes large. In Patent Document 3, a spherical lens or an elliptic lens is used as a biconvex cylindrical lens. As shown in FIG. 9 of Patent Document 3, the viewing angle at which the stray light region can be reduced to 10% or less is ± 22.5 degrees. This viewing angle is about the same as the viewing angle of 0.37 radians (± 21 degrees) of the lenticular lens of FIG. As shown in FIG. 10 of Patent Document 3, the viewing angle at which crosstalk can be reduced to 2 pixels or less is ± 15 degrees.

For a more stable stereoscopic image, a wider viewing angle is desired that is small enough to allow stray light and crosstalk. The lens shape may be an aspherical surface such as an ellipse, a parabola, or a hyperbola, but the design is facilitated if those aspherical shapes can be specified as much as possible.

In order to solve the conventional problems, an image display object of the present invention has an image display surface, a first panel in which an array of first concave lenses is formed on one side, and an array of second concave lenses on one side. The first and second concave lenses are disposed opposite to each other, and the refractive index of the first panel and the second panel is different between the first concave lens and the second concave lens. A substance is provided, and the first concave lens shape can be approximated by the following equation:
T + X ² / [R + (R ² −kX ² ) ^1/2 ]
In addition, k has a value of −0.5 <k <0.5. As a result, the viewing angle of the stereoscopic image can be enlarged.

  Furthermore, it is preferable that k has a value of 0.16 <k <0.5 or −0.5 <k <−0.16. This makes it possible to reduce the cost by reducing the thickness of the biconvex cylindrical lens.

Alternatively, the image display object of the present invention has an image display surface, a first panel in which an array of first concave lenses is formed on one side, and a second panel in which an array of second concave lenses is formed on one side. The first and second concave lenses are arranged to face each other, and a substance having a refractive index different from that of the first panel and the second panel is provided between the first concave lens and the second concave lens, and the first concave lens The shape can be approximated by
T- [1 / {12R (ρW) ² }] · X ⁴ + [1 / (2R)] · X ²
And ρ has a value of 0.2 <ρ <0.7. As a result, the viewing angle of the stereoscopic image can be increased, and the thickness of the biconvex cylindrical lens can be reduced to reduce the cost.

In the image display object of the present invention, the distance from the image display surface to the bottom of the first concave lens is T, the radius of curvature near the lens center line of the first concave lens is R, and the refractive index of the first panel is n1, the refractive index of the substance between the first concave lens and the second concave lens is n2, ε = n2 / n1, and the distance D between the bottom of the first concave lens and the top of the second concave lens is approximately:
D = R [ε / (ε-1)] [R-2 (ε-1) T] / [R- (ε-1) T]
It has the value of. As a result, the viewing angle of the stereoscopic image can be expanded, and the design of the image display object is facilitated.

Alternatively, in the image display object according to the present invention, the radius of curvature near the lens center line of the first concave lens is R, the refractive index of the first panel is n1, and the refraction of the substance between the first concave lens and the second concave lens is performed. The rate is n2, the distance between the bottom of the first concave lens and the top of the second concave lens is D, ε = n2 / n1, and the distance from the image display surface to the bottom of the first concave lens is
D = R [ε / (ε-1)] [R-2 (ε-1) T] / [R- (ε-1) T]
It is characterized by having a value larger than T that satisfies This can improve the parallelism of the emitted light.

  Moreover, it is preferable that the image display thing of this invention does not display an image on the image display surface corresponding to the boundary of the said 1st concave lens adjacent to each other. As a result, the viewing angle of the stereoscopic image can be enlarged.

  Moreover, it is preferable that the image display thing of this invention provides an antireflection function in the plane on the opposite side to the said 2nd concave lens of the said 2nd panel. This makes it easier to see the three-dimensional sign.

  The image display object of the present invention is characterized by having a portion for switching between a stereoscopic image and a planar image and a portion for always displaying a planar image. As a result, even when viewing a stereoscopic image, small characters can be displayed.

  ADVANTAGE OF THE INVENTION According to this invention, the image display apparatus which can switch stably a high-resolution planar image and a stereo image with a wide viewing angle can be provided. Further, it is possible to provide a stereoscopic image printed material having a wide viewing angle and smooth both surfaces.

Sectional drawing of the image display apparatus of this invention. Sectional drawing of the image printed matter of this invention. The figure explaining analytically the principle of the three-dimensional image display in the image display apparatus of this invention. The figure which shows a stray light. The figure which shows the case where the upper and lower lens boundaries contact | connect in the image display apparatus of this invention. The figure which shows the coefficient of the panel structure with respect to elliptic lens shape in Embodiment 1 of this invention. The figure which shows the viewing angle with respect to elliptic lens shape in Embodiment 1 of this invention. The simulation result of the viewing angle with respect to the case where the refractive index of the biconvex elliptical lens in Embodiment 1 of this invention is 1.62. The simulation result of the viewing angle with respect to the case where the refractive index of the biconvex elliptical lens in Embodiment 1 of this invention is 1.7. The figure which shows the coefficient of the panel structure with respect to the hyperbolic lens shape in Embodiment 2 of this invention. The figure which shows the viewing angle with respect to the hyperbola lens shape in Embodiment 2 of this invention. The simulation result of the viewing angle with respect to the case where the refractive index of the biconvex hyperbolic lens in Embodiment 2 of this invention is 1.62. Explanatory drawing of the light emitted from the point ((delta) = W / 2) of an image display surface with respect to the case where the refractive index of the biconvex hyperbola lens in Embodiment 2 of this invention is 1.62. The simulation result of the viewing angle with respect to the case where the refractive index of the biconvex hyperbolic lens in Embodiment 2 of this invention is 1.7. The figure which shows the coefficient of the panel structure with respect to the 4th order even number lens shape in Embodiment 3 of this invention. The figure which shows the viewing angle with respect to the 4th order even number lens shape in Embodiment 3 of this invention. The simulation result of the viewing angle with respect to the case where the refractive index of the biconvex fourth order even number lens in Embodiment 3 of this invention is 1.7. The simulation result of the viewing angle with respect to the case where the refractive index of the biconvex hyperbolic lens in Embodiment 4 of this invention is 1.62. Explanatory drawing of a liquid-crystal characteristic in case a polarization direction is parallel to the major axis of a liquid crystal molecule. Explanatory drawing of the liquid-crystal characteristic in case a polarization direction is perpendicular | vertical to the long axis of a liquid crystal molecule. Explanatory drawing of switching of the plane image and the stereo image in Embodiment 5 of this invention. Sectional drawing of the image display apparatus which shows the specific example in Embodiment 6 of this invention. The pixel arrangement | sequence figure in Embodiment 6 of this invention which shows a specific example. The simulation result in Embodiment 7 of this invention. Sectional drawing of the image display apparatus in Embodiment 7 of this invention. Sectional drawing of the image display apparatus in Embodiment 8 of this invention. The block diagram of the image display apparatus which has a part which always displays a planar image in Embodiment 9 of this invention. The perspective view of a lenticular lens. Sectional drawing of the image display apparatus using a lenticular lens. The figure which shows the imaging method of a multiview image. 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 a lenticular lens. The principle figure of the stereoscopic vision with respect to the changed position of the right and left eyes using a lenticular lens. An analytical explanatory diagram of a spherical lenticular lens. The figure which shows the angle of an ideal emitted light. Simulation result of spherical lenticular lens. Explanatory drawing of the light ray emitted from the point ((delta) = W / 4) of an image surface at the time of using a spherical lenticular lens. Explanatory drawing of the light ray which comes out from the point ((delta) = W / 2) of an image surface at the time of using a spherical lenticular lens. Sectional drawing of the image display apparatus which can switch the planar image and stereoscopic image using the conventional single convex lens. Sectional drawing of the image display apparatus which can switch the planar image and stereoscopic image using the conventional biconvex lens.

DESCRIPTION OF SYMBOLS 101 1st panel 102 2nd panel 103 Biconvex cylindrical lens 104 Image display part 105 Transparent panel 201 1st panel 202 2nd panel 203 Biconvex cylindrical lens 204 Image display part 301 1st panel 302 1st cylindrical lens surface 303 2nd Panel 304 Second cylindrical lens surface 305 Biconvex cylindrical lens 306 Image display unit 307 Lens center line 308 Virtual surface 401 Light beam desirable for stereoscopic image display 402 Light beam desirable for stereoscopic image display 403 Stray light 2500 Image 2600 Second panel surface 2701 Image display Device 2702 Display unit for switching between stereoscopic image and planar image 2703 Display surface for displaying planar image 2801 Cylindrical lens 2901 Lenticular lens 2902 Image display unit 29 3 transparent panel 3401 a cylindrical lens 3402 image plane 3403 lens centerline 3901 Katatotsu lens array 3902 image display unit 3903 transparent panel 4001 biconvex lens array 4002 image display unit 4003 transparent panel

  The outline of the present invention will be described below with reference to the drawings.

  FIG. 1 is a cross-sectional view of an image display device of the present invention. In FIG. 1, 101 is a first panel provided with an array of concave cylindrical lenses on one side, and 102 is a second panel provided with an array of concave cylindrical lenses on one side. The concave cylindrical lens 101 and the concave cylindrical lens 102 are arranged to face each other. Reference numeral 103 denotes an array of biconvex cylindrical lenses provided between the first panel 101 and the second panel 102. Reference numeral 104 denotes an image display unit, and reference numeral 105 denotes a transparent panel for protecting the image display unit. When the panel 101 and the transparent panel 103 are made of general glass or resin, their refractive indexes are approximately the same, and the first panel 101 and the transparent panel 103 are handled optically and integrally.

In FIG. 1, in order to switch between a planar image and a stereoscopic image, the refractive index of the substance of the biconvex cylindrical lens array 103 changes electrically, or the substance of the biconvex cylindrical lens array 103 changes in the polarization direction of light. On the other hand, the anisotropy is different in refractive index. A liquid crystal can be considered as such a substance. The refractive index of liquid crystal varies depending on the polarization direction of light and the alignment direction of liquid crystal molecules. As an example, the refractive index changes from about 1.5 to about 1.62 for visible wavelengths at ambient temperatures of 20 to 40 degrees. When the refractive index of the substance of the biconvex cylindrical lens array is large, a stereoscopic image is displayed, and when the refractive index is small, a planar image is displayed. The small refractive index of the material of the biconvex cylindrical lens array can be selected to be approximately the same as the refractive index of the material of the first panel 101 and the second panel 102. FIG. 1 is similar to FIG. 40 of the conventional example, but in the image display apparatus of the present invention, in order to widen the viewing angle of the stereoscopic image, the lens shape, the distance between the image display surface and the biconvex cylindrical lens, the biconvex cylindrical lens. Optimize lens thickness.

  FIG. 2 is a cross-sectional view of the printed image according to the present invention. In FIG. 2, 201 is a first panel (or sheet) provided with an array of concave cylindrical lenses on one side, and 202 is a second panel (or sheet) provided with an array of concave cylindrical lenses on one side. The concave cylindrical lens 201 and the concave cylindrical lens 202 are arranged to face each other. Reference numeral 203 denotes an array of biconvex cylindrical lenses provided between the first panel 201 and the second panel 202. Reference numeral 204 denotes an image printing unit.

In the printed matter as shown in FIG. 2, it is not necessary to switch between the stereoscopic image and the planar image, the stereoscopic image is always displayed, the refractive index of the material of the biconvex cylindrical lens array, the refractive index of the material of the first panel 201 and the second panel 202. Greater than rate. As such a high refractive index material, a nanocomposite resin in which dielectric fine particles such as titanium oxide, zirconium oxide, and zinc oxide are mixed with a general resin can be considered, and a resin having a refractive index of about 1.7 can be synthesized. In the image printed matter of the present invention, in order to widen the viewing angle of the stereoscopic image, the lens shape, the interval between the image display surface and the biconvex cylindrical lens, the thickness of the biconvex cylindrical lens, and the like are optimized.

  The first method of enlarging the viewing angle is to increase the refractive index of the array 103 or 203 of biconvex cylindrical lenses. However, there is a limit to the change in the refractive index of the liquid crystal. The development of a material with a larger electrical refractive index change is awaited. In addition, the refractive index of the nanocomposite resin also has a limit.

  A second method for enlarging the viewing angle is to increase the width of the cylindrical lens. In the spherical lens and the elliptical lens used in Patent Document 1 and Patent Document 3, when the width of the cylindrical lens is increased, the gradient around the lens increases, the angle of the light beam refracted on the lens surface changes greatly, and the parallelism of the emitted light Deteriorates. Although the elliptic lens can be made flatter to increase the cylindrical lens width, there is a limit to the flatness. Improvement or optimization of the lens shape is desired.

  An analysis method will be described with reference to FIG. 3 as to what lens shape is used to enlarge the viewing angle. For this analysis, the same ray tracing method as that in FIG. 34 is used. In FIG. 3, 301 is a first panel having a cylindrical lens surface 302 formed on one side, and 303 is a second panel having a cylindrical lens surface 304 formed on one side. An array 305 of biconvex cylindrical lenses is formed between 302 and 304. Reference numeral 306 denotes an image display surface, and reference numeral 307 denotes a lens center line of the cylindrical lens. In FIG. 3, the panel 101 and the transparent panel 103 of FIG. The distance from the image display surface 306 to the bottom of the cylindrical lens surface 302 is T, the maximum thickness of the biconvex cylindrical lens 305 (the distance between the bottom of the lens surface 302 and the top of the lens surface 304) is D, and the lens centerline of the cylindrical lens The radius of curvature in the vicinity is R, and the width of one cylindrical lens is W. The refractive index of the first panel 301 is approximately the same as the refractive index of the second panel 303 and is n1, and the refractive index of the biconvex cylindrical lens array 305 is n2.

  Let P1 be a point at which light emitted from a point on the image display surface 306 at a distance δ from the lens center line 307 is incident on the cylindrical lens surface 302, and let P2 be a point at which the light is incident on the cylindrical lens surface 304. Thereafter, the light is emitted from the observation side surface of the second panel 303. The shape of the cylindrical lens surface 302 is represented as F (X), and the shape of the opposing cylindrical lens surface 304 is represented as G (X).

  In FIG. 3, reference numeral 308 denotes a virtual surface. In the prior application by the inventor of the present invention (International Patent Publication No. WO2008-114813), the upper cylindrical lens is considered to have a configuration opposite to that in FIG. 3, and the lens medium is refracted on a plane corresponding to the virtual plane 308 in FIG. Simulation is also performed when the rates are different. In the present invention, the medium is the same above and below the virtual plane, and the position coordinates (Q) on the virtual plane have no meaning. In the present invention, the same simulation technique as that of the prior application is used. Accordingly, in the simulation described later, the position coordinate (Q) where the light emitted from the image display surface 306 enters the virtual surface 308 is used as a means for indicating the traveling direction of the light.

The angle θ of the light ray from the point on the image display surface (distance δ from the lens center line 307) to the point of the position coordinate Q of the virtual surface 308 (distance Q from the lens center line 307) is obtained by (Equation 16). This ray enters the point P1 (distance X1 from the lens center line 307) without changing the direction on the virtual plane. The X coordinate (X1) of the point P1 is obtained by solving the equation (Equation 17). The gradient of the lens surface at the point P1 is a differential coefficient of the function F (X) and is obtained by (Equation 18). The incident angle α to the lens surface F (X) is obtained by (Equation 19), and the emission angle β is obtained by (Equation 20) from the law of refraction. The light ray from the point P1 to the point P2 is expressed by (Expression 21), and the X coordinate (X2) of the point P2 is obtained by solving the equation (Expression 22). The gradient of the lens surface at the point P2 is a differential coefficient of the function G (X) and is obtained by (Equation 23). The incident angle φ to the lens surface G (X) is obtained by (Equation 24), and the emission angle ψ is obtained by (Equation 25) from the law of refraction. The incident angle ζ on the observation side surface of the panel 303 is obtained by (Equation 26), and the exit angle ν from the panel 303 is obtained by (Equation 27) from the law of refraction. Here, the differential coefficient of G (X) at the point P2 becomes negative if X is a positive value (the algebraic angle is negative, τ <0). In order to show the geometric angle as a positive value, the inclination of the tangent line at the point P2 is represented as (−τ) in FIG.
(Equation 16) tan θ = (δ−Q) / T
(Expression 17) F (X) · tan θ = (δ−X)
(Equation 18) tanκ = dF (X) / dX (X = X1)
(Equation 19) α = κ−θ
(Expression 20) n2 · sin β = n1 · sin α
(Expression 21) YF (X1) =-(X-X1) .cot (κ-β)
(Equation 22) G (X) −F (X1) = − (X−X1) · cot (κ−β)
(Equation 23) tan (−τ) = − dG (X) / dX (X = X2)
(Equation 24) φ = (− τ) + (κ−β)
(Equation 25) n2 · sinφ = n1 · sinψ
(Equation 26) ζ = ψ − (− τ)
(Expression 27) sinν = n1 · sinζ

  If a point on the image display surface (distance δ from the lens center line 307) and a position coordinate Q on the virtual surface are given, from (Equation 16) to (Equation 27), θ, X1, κ, α, β, X2, τ, φ, ψ, ζ, and ν are obtained, and the direction of the light emitted from the panel 303 is obtained.

First, consider paraxial approximation with a small angle. Functions F (X) and G (X) representing the lens shape are approximated by (Equation 28) and (Equation 29). In the vicinity of the lens center line 307, the lens shape is well approximated to a spherical surface, the curvature is (1 / R), and the differential coefficients [dF (X) / dX] and [dG (X) / dX] representing the gradient are used. Is expressed by (Equation 30) and (Equation 31).
(Equation 28) F (X) = T
(Equation 29) G (X) = T + D
(Expression 30) dF (X) / dX = X / R
(Equation 31) dG (X) / dX = −X / R

Using these, in the paraxial approximation, (Equation 16) to (Equation 27) are approximated as (Equation 32) to (Equation 42), respectively. In paraxial approximation, X1 = Q, and (Equation 16) and (Equation 17) are similarly approximated by (Equation 32).
(Equation 32) θ = (δ−X1) / T
(Expression 33) κ = X1 / R
(Equation 34) α = κ−θ
(Expression 35) n2 · β = n1 · α
(Equation 36) YT = − (X−X1) / (κ−β)
(Equation 37) (T + D) −T = − (X2−X1) / (κ−β)
(Equation 38) τ = −X2 / R
(Equation 39) φ = (− τ) + (κ−β)
(Equation 40) n2 · φ = n1 · ψ
(Equation 41) ζ = ψ − (− τ)
(Expression 42) ν = n1 · ζ

The lenticular lens effect, that is, the condition that light emitted from a point on the image display surface (distance δ from the lens center line 307) becomes substantially parallel light with a constant emission angle is that ν does not depend on θ. At least, the paraxial approximation needs to satisfy the lenticular effect well. In this case, the maximum thickness D of the biconvex cylindrical lens 305 (the distance between the bottom of the lens surface 302 and the top of the lens surface 304) D is given by (Equation 43) and (Equation 44). Here, ε = n2 / n1. The maximum thickness D is determined by n1, n2, and T.
(Equation 43) D = [ε / (ε−1)] RΔ
(Expression 44) Δ = [R−2 (ε−1) T] / [R− (ε−1) T]

  Here, an outline of a desirable shape of the biconvex cylindrical lens of FIGS. 1 to 3 will be described. The materials of the array 103 of the biconvex cylindrical lens in FIG. 1 have anisotropy that changes in refractive index electrically or has a different refractive index with respect to the polarization direction of light. A liquid crystal can be considered as such a material, but it is preferable that the maximum thickness (D in FIG. 3) of the biconvex cylindrical lens 103 is thin for cost reduction. When the refractive index is electrically changed, the applied voltage can be reduced, so that the thinner one is more desirable. The material of the array 203 of the biconvex cylindrical lens in FIG. 2 is a nanocomposite resin having a high refractive index. Nanocomposite resin is expensive, and it is better to reduce the maximum thickness (D in FIG. 3) of the biconvex cylindrical lens 203 for cost reduction.

  The stray light from an erroneous pixel will be described with reference to FIG. In FIG. 4, the same components as those in FIG. Reference numerals 401 and 402 are desirable light beams for viewing a stereoscopic image, and light emitted from an image plane corresponding to a focused cylindrical lens is refracted and emitted from the focused cylindrical lens surfaces. Reference numeral 403 denotes stray light, and light emitted from an image plane corresponding to an adjacent cylindrical lens is refracted by an adjacent lower cylindrical lens surface and refracted and emitted by an upper cylindrical lens surface of interest. The stray light 403 is similar in emission direction to the desired light rays 401 and 402 and degrades the image quality. If the interval between the lower cylindrical lens and the upper cylindrical lens is wide at the boundary between them, stray light generally increases. Therefore, it is desirable that the upper and lower cylindrical lenses are in contact with each other as much as possible at the boundary between them.

FIG. 5 shows a case where the lower cylindrical lens and the upper cylindrical lens are in contact with each other at their boundary portions. In FIG. 5, no stray light is generated.
(Embodiment 1)

First, consider an elliptic lens. In general, the lens shapes F (X) and G (X) are expressed by (Equation 45) and (Equation 46), and k> 0 in the case of an ellipse. It is more convenient to express these equations as in (Equation 47) and (Equation 48) in order to solve the above (Equation 17) and (Equation 22). Here, m = 1 / k. In addition, the function of the upper and lower cylindrical lens surfaces needs the condition of (Equation 49) to form a biconvex lens shape, and this condition is expressed as (Equation 50).
(Equation 45) F (X) = T + X ² / [R + (R ² −kX ² ) ^1/2 ]
(Equation 46) G (X) = T + D−X ² / [R + (R ² −kX ² ) ^1/2 ]
(Equation 47) F (X) = T + (mR) − [(mR) ² −m · X ² ] ^1/2
(Equation 48) G (X) = T + D− (mR) + [(mR) ² −m · X ² ] ^1/2
(Equation 49) G (W / 2)> F (W / 2)
(Equation 50) D> 2 mR-2 [(mR) ² −m · (W / 2) ² ] ^1/2

  In an image display device capable of switching between a flat image and a stereoscopic image, for example, the refractive index of the first panel and the second panel is 1.5, and the refractive index of the biconvex cylindrical lens array between them is electrically changed. Or anisotropy that varies depending on the polarization direction of light. A liquid crystal molecule can be considered as such a substance. A liquid crystal molecule having a smaller refractive index of 1.5 which is about the same as that of the surrounding medium and a larger refractive index of 1.62 can be selected. Further, in the stereoscopic image printed matter, it is not necessary to switch between the planar image and the stereoscopic image, and a high refractive index resin is used as the material of the biconvex cylindrical lens array. As such a high refractive index resin, a nanocomposite resin in which dielectric fine particles such as titanium oxide, zirconium oxide, or zinc oxide are mixed with an ultraviolet curable resin can be considered. It is possible to synthesize a resin having a refractive index of 1.7.

An elliptical shape is determined for each value of m (= 1 / k). In the first embodiment, the cylindrical lens width W is 75% of the length of the axis parallel to the elliptical image display surface. In (Equation 43) and (Equation 44), if the distance T from the image display surface to the bottom of the lower cylindrical lens surface is generally increased, the maximum thickness of the biconvex cylindrical lens (the bottom of the lower cylindrical lens surface and the upper cylindrical lens is increased). The distance (D) between the tops of the surfaces becomes smaller. As described above, both the liquid crystal and the nanocomposite resin are expensive, and the smaller the D, the lower the cost. Also, the smaller the D, the less the stray light described above. As shown in FIG. 5, when the upper and lower lens surfaces are in contact with each other at the boundary of the cylindrical lens, D becomes the smallest, and T at that time can be obtained. In this case, stray light is eliminated.

FIG. 6 shows the values of W, D, T1, and T2 when m (= 1 / k) is changed. These values satisfy the conditions (Equation 43), (Equation 44), and (Equation 50). Here, R = 1 is standardized, W is a value of 75% of the length of the axis parallel to the elliptical image display surface, and T is a value when the upper and lower lens surfaces are in contact with each other at the boundary of the cylindrical lens. T1 is the case where the refractive index of the biconvex cylindrical lens is 1.62, and T2 is the case where the refractive index is 1.7.

  FIG. 7 shows a viewing angle (radian) when m (= 1 / k) is changed. To obtain the viewing angle, simulation is performed using (Equation 16) to (Equation 27). In FIG. 3, n1 = 1.5 and R = 1, and W, D, T1, and T2 obtained in FIG. 6 are used for each value of m. (Equation 17) and (Equation 22) become a quadratic equation of X using (Equation 47) and (Equation 48), and a solution can be obtained algebraically. FIG. 7 shows a case where the refractive index of the biconvex cylindrical lens is 1.62 and 1.7.

As can be seen from FIG. 7, in the range where the value of m (= 1 / k) is smaller than 2, the viewing angle is remarkably reduced. Therefore, it is desirable to satisfy (Equation 51) in the ellipses represented by (Equation 47) and (Equation 48). Alternatively, it is desirable to satisfy (Equation 52) in the ellipses represented by (Equation 45) and (Equation 46).
(Equation 51) m> 2
(Equation 52) k <0.5

6 and 7 show simulation results when normalized with R = 1. In actual design, the width W of the cylindrical lens is often used as a reference. For example, W = 423 μm for 60 cylindrical lenses per inch (60 lpi), and W = 254 μm for 100 lenses per inch (100 lpi). R, T, D, etc. are determined for these W values. As described above, the value of D is preferably small for cost reduction, and preferably smaller than W if possible. For that purpose, it is desirable that the value of m is smaller than 6 from FIG. 6, and it is desirable to satisfy (Equation 53) and (Equation 54) in consideration of the condition.
(Formula 53) 2 <m <6
(Formula 54) 0.16 <k <0.5

  Next, FIG. 8 shows a simulation result of the emission angle for a typical m = 4 (k = 0.25) in the case of n2 = 1.62. From FIG. 6, T = 5.6, W = 3, and D = 2.7. The horizontal axis represents position coordinates (Q) where light emitted from a point on the image display surface enters the virtual surface 308, and the vertical axis represents the angle (ν) emitted from the second panel 303. As the points on the image display surface (distance δ from the lens center line 307), 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 display surface corresponding to the adjacent cylindrical lens.

  The following can be understood from FIG. The light flux from each point on the image display surface toward the cylindrical lens surface 302 is emitted from the second panel as substantially parallel light from the center of each light flux. It becomes non-parallel light. As for the light beam from the point (δ> W / 2) on the image plane corresponding to the adjacent cylindrical lens, the light at each central portion becomes substantially parallel light, but the light at each peripheral portion becomes non-parallel light. These non-parallel lights have a large change in the emission angle ν with respect to the horizontal axis (incident position Q on the imaginary plane), and the amount of light when viewed from a specific emission angle is small. That is, when viewed from one direction, the intensity of these non-parallel lights is small and almost parallel lights are seen. The viewing angle is ± 0.33 radians (± 19 degrees).

FIG. 9 shows a simulation result of the emission angle for a typical m = 4 (k = 0.25) in the case of n2 = 1.7. From FIG. 6, T = 3, W = 3, and D = 2.7. The horizontal axis represents the position coordinates (Q) where light emitted from a point on the image display surface enters the virtual surface 308, and the vertical axis represents the angle (ν) emitted from the second panel 303. As the points on the image display surface (distance δ from the lens center line 307), 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 display surface corresponding to the adjacent cylindrical lens. FIG. 9 shows the same tendency as FIG. 8, but since the refractive index is large, the emission angle is also large. The viewing angle is ± 0.50 radians (± 29 degrees).
(Embodiment 2)

Next, consider a hyperbolic lens. In general, the lens shapes F (X) and G (X) are expressed by (Equation 55) and (Equation 56), and in the case of a hyperbola, k <0. It is more convenient to express these equations as in (Equation 57) and (Equation 58) in order to solve the above (Equation 17) and (Equation 22). Here, m = −1 / k. Further, the function of the upper and lower cylindrical lens surfaces needs the condition of (Equation 59) to form a biconvex lens shape, and this condition is expressed as (Equation 60).
(Expression 55) F (X) = T + X ² / [R + (R ² −kX ² ) ^1/2 ]
(Expression 56) G (X) = T + D−X ² / [R + (R ² −kX ² ) ^1/2 ]
(Equation 57) F (X) = T− (mR) + [(mR) ² + m · X ² ] ^1/2
(Formula 58) G (X) = T + D + (mR) − [(mR) ² + m · X ² ] ^1/2
(Equation 59) G (W / 2)> F (W / 2)
(Equation 60) D> 2 [(mR) ² −m · (W / 2) ² ] ^1/2 −2 mR

  In the image display apparatus capable of switching between a planar image and a stereoscopic image, the refractive index of the first panel and the second panel is 1.5 as in the first embodiment, and the biconvex cylindrical lens array between them is a liquid crystal molecule. Fill with. A liquid crystal molecule having a smaller refractive index of 1.5 which is about the same as that of the surrounding medium and a larger refractive index of 1.62 can be selected. Further, in the stereoscopic image printed matter, it is not necessary to switch between the planar image and the stereoscopic image, and the biconvex cylindrical lens array is filled with the nanocomposite resin. It is possible to synthesize a resin having a refractive index of 1.7.

The hyperbolic shape is determined for each value of m (= −1 / k). In the hyperbolic lens, the gradient around the lens is gentler than that of the elliptical lens, and the cylindrical lens width W can be increased. When the refractive index of the biconvex cylindrical lens is 1.62, consider W = 5. However, if the refractive index of the biconvex cylindrical lens is too large, the refraction angle becomes too large. When the refractive index is 1.7, consider W = 4. In (Equation 43) and (Equation 44), if the distance T from the image display surface to the bottom of the lower cylindrical lens surface is generally increased, the maximum thickness of the biconvex cylindrical lens (the bottom of the lower cylindrical lens surface and the upper cylindrical lens is increased). The distance (D) between the tops of the surfaces becomes smaller. As described above, both the liquid crystal and the nanocomposite resin are expensive, and the smaller the D, the lower the cost. Also, the smaller the D, the less the stray light described above. As shown in FIG. 5, when the upper and lower cylindrical lens surfaces are in contact with each other at the boundary of the cylindrical lens, D becomes the smallest, and T at that time can be obtained. In this case, stray light is eliminated.

FIG. 10 shows values of W, D, T1, and T2 when m (= −1 / k) is changed. These values satisfy the conditions (Equation 43), (Equation 44), and (Equation 60). Here, normalization is performed with R = 1, and T is a value when the upper and lower lens surfaces are in contact with each other at the boundary of the cylindrical lens. T1 is the case where the refractive index of the biconvex cylindrical lens is 1.62, and T2 is the case where the refractive index is 1.7.

  FIG. 11 shows a viewing angle (radian) when m (= −1 / k) is changed. To obtain the viewing angle, simulation is performed using (Equation 16) to (Equation 27). In FIG. 3, n1 = 1.5 and R = 1, and W, D, T1, and T2 obtained in FIG. 10 are used for each value of m. (Equation 17) and (Equation 22) become a quadratic equation of X using (Equation 57) and (Equation 58), and a solution can be obtained algebraically. FIG. 11 shows a case where the refractive index of the biconvex cylindrical lens is 1.62 and 1.7.

As can be seen from FIG. 11, in the range where the value of m (= −1 / k) is smaller than 2, the viewing angle is remarkably reduced. Therefore, it is desirable to satisfy (Equation 61) in the hyperbola expressed by (Equation 57) and (Equation 58). Alternatively, it is desirable to satisfy (Equation 62) in the hyperbola represented by (Equation 55) and (Equation 56).
(Equation 61) m> 2
(Equation 62) k> −0.5

10 and 11 show the simulation results when R = 1. In actual design, as in the first embodiment, the cylindrical lens width W is often used as a reference, and values such as R, T, and D are determined with respect to the value of W. As described above, the value of D is preferably small for cost reduction, and preferably smaller than W if possible. For that purpose, it is desirable that the value of m is smaller than 6 from FIG. 10, and it is desirable to satisfy (Equation 63) and (Equation 64) in consideration of the condition.
(Equation 63) 2 <m <6
(Formula 64) −0.5 <k <−0.16

  Next, FIG. 12 shows a simulation result of the emission angle for a typical m = 4 (k = −0.25) when n2 = 1.62. From FIG. 10, T = 4.9, W = 5, and D = 4.8. The horizontal axis represents position coordinates (Q) where light emitted from a point on the image display surface enters the virtual surface 308, and the vertical axis represents the angle (ν) emitted from the second panel 303. Four cases of 0, W / 4, W / 2, and 3W / 4 are shown as points on the image display surface (distance δ from the lens center line 307). δ = 3W / 4 is light from a point on the image display surface corresponding to the adjacent cylindrical lens.

  The following can be understood from FIG. Light exiting from the lens center (δ = 0) on the image display surface becomes substantially parallel light with an exit angle of approximately ν = 0. The substantially parallel light has a tendency that the curve representing the emission angle (ν) is slightly inclined with respect to the horizontal axis (Q) and slightly spreads. The light emitted from the W / 4 point (δ = W / 4) from the lens center line of the image display surface is non-parallel light when entering the left end of the lens surface, but entering other lens surfaces. Becomes substantially parallel light having an emission angle near ν = 0.25. The curve representing the substantially parallel light is also slightly lower right and tends to spread. Light coming out from the boundary of adjacent cylindrical lenses (δ = W / 2) also becomes non-parallel light when entering the left end of the lens surface, and the emission angle changes rapidly, but when entering the other lens surface The emission angle changes gradually from ν = 0.60 to ν = 0.46. This is shown in FIG. Although not perfectly parallel light, most of the light rays are emitted in the viewing direction.

  Images from many viewpoints are displayed on the image display surface 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, the smallest exit angle of the light exiting from the boundary between adjacent cylindrical lenses and exiting from the panel with a relatively high intensity determines the viewing angle. In FIG. 12, the viewing angle is ± 0.46 radians (± 26 degrees). It can be seen that the viewing angle can be expanded by making the lens shape a hyperbola.

FIG. 14 shows a simulation result of the emission angle for a typical m = 2 (k = −0.5) in the case of n2 = 1.7. From FIG. 10, T = 3, W = 4, and D = 2.9. The horizontal axis represents position coordinates (Q) where light emitted from a point on the image display surface enters the virtual surface 308, and the vertical axis represents the angle (ν) emitted from the second panel 303. Four cases of 0, W / 4, W / 2, and 3W / 4 are shown as points on the image display surface (distance δ from the lens center line 307). δ = 3W / 4 is light from a point on the image display surface corresponding to the adjacent cylindrical lens. FIG. 14 shows the same tendency as FIG. 12, but the exit angle is also increased because the refractive index is large. The viewing angle is ± 0.62 radians (± 36 degrees).
(Embodiment 3)

  When the lens shape is an ellipse, as shown in FIGS. 8 and 9, the curve representing the emission angle (ν) is horizontal with respect to the incident position (Q), and the parallelism of the emitted light is high. When the lens shape is a hyperbola, as shown in FIGS. 12 and 14, the curve representing the emission angle (ν) is slightly lower to the incident position (Q), and the emitted light has a tendency to slightly expand. The viewing angle can be expanded. On the lens surface away from the lens center line, the ellipse has a smaller radius of curvature than the hyperbola. Therefore, it can be expected that the lens shape having a slightly smaller radius of curvature than the hyperbola can have a large viewing angle and high parallelism.

  A parabola can be considered as an intermediate shape between an ellipse and a hyperbola. In general, the lens shapes F (X) and G (X) are expressed by (Equation 45), (Equation 46), (Equation 55), and (Equation 56). In the case of a parabola, k = 0 and the value of m Is infinite. As can be seen from FIGS. 6 and 10, D increases with respect to W as the value of m increases.

In the third embodiment, the lens shape is approximated by a polynomial composed only of X to the even power. The coefficient of X ² is 1 / (2R) using the radius of curvature R in the vicinity of the lens center line. Further, X ⁶ or more coefficients are omitted as very small. If the X coordinate of the inflection point is ρW, this quaternary even function is expressed by (Equation 65) and (Equation 66). Further, in order for the upper and lower cylindrical lens surfaces to form a biconvex lens, the condition of (Equation 67) is necessary, and this condition is expressed as (Equation 68).
(Expression 65) F (X) = T− [1 / {12R (ρW) ² }] · X ⁴
+ [1 / (2R)] · X ²
(Equation 66) G (X) = T + D + [1 / {12R (ρW) ² }] · X ⁴
-[1 / (2R)] · X ²
(Equation 67) G (W / 2)> F (W / 2)
(Number ^{68) D> W 2 / (} 4R) -W 2 / (96Rρ 2)

  In the image display device capable of switching between a planar image and a stereoscopic image, the refractive index of the first panel and the second panel is 1.5 as in the first and second embodiments, and a biconvex cylindrical lens array between them is used. Fill with liquid crystal molecules. A liquid crystal molecule having a smaller refractive index of 1.5 which is about the same as that of the surrounding medium and a larger refractive index of 1.62 can be selected. Further, in the stereoscopic image printed matter, it is not necessary to switch between the planar image and the stereoscopic image, and the biconvex cylindrical lens array is filled with the nanocomposite resin. It is possible to synthesize a resin having a refractive index of 1.7.

A quaternary even number shape is determined for each value of ρ. In the fourth-order even-number lens, the gradient around the lens is gentler than that of the elliptic lens depending on the position of the inflection point, and the cylindrical lens width W can be increased. When the refractive index of the biconvex cylindrical lens is 1.62, consider W = 5. However, if the refractive index of the biconvex cylindrical lens is too large, the refraction angle becomes too large. When the refractive index is 1.7, consider W = 4. In (Equation 43) and (Equation 44), if the distance T from the image display surface to the bottom of the lower cylindrical lens surface is generally increased, the maximum thickness of the biconvex cylindrical lens (the bottom of the lower cylindrical lens surface and the upper cylindrical lens is increased). The distance (D) between the tops of the surfaces becomes smaller. As described above, both the liquid crystal and the nanocomposite resin are expensive, and the smaller the D, the lower the cost. Also, the smaller the D, the less the stray light described above. As shown in FIG. 5, when the upper and lower cylindrical lens surfaces are in contact with each other at the boundary of the cylindrical lens, D becomes the smallest, and T at that time can be obtained. In this case, stray light is eliminated.

FIG. 15 shows the values of W, D, T1, and T2 when the value of ρ is changed. These values satisfy the conditions (Equation 43), (Equation 44), and (Equation 68). Here, normalization is performed with R = 1, and T is a value when the upper and lower lens surfaces are in contact with each other at the boundary of the cylindrical lens. T1 is the case where the refractive index of the biconvex cylindrical lens is 1.62, and T2 is the case where the refractive index is 1.7.

  FIG. 16 shows the viewing angle (radian) when the value of ρ is changed. To obtain the viewing angle, simulation is performed using (Equation 16) to (Equation 27). In FIG. 3, n1 = 1.5 and R = 1, and W, D, T1, and T2 obtained in FIG. 15 are used for each value of ρ. (Equation 17) and (Equation 22) become a quaternary equation of X using (Equation 65) and (Equation 66), and a solution can be obtained algebraically using the Ferrari solution. FIG. 16 shows a case where the refractive index of the biconvex cylindrical lens is 1.62 and 1.7.

15 and 16 show the simulation results when R = 1. In actual design, as in the first and second embodiments, the cylindrical lens width W is often used as a reference, and values such as R, T, and D are determined with respect to the value of W. As described above, the value of D is preferably small for cost reduction, and preferably smaller than W if possible. For this purpose, the value of ρ is preferably smaller than 0.7 from FIG. That is, it is desirable to satisfy (Equation 69).
(Equation 69) 0.2 <ρ <0.7

  Next, FIG. 17 shows a simulation result of the emission angle with respect to a typical ρ = 0.45 in the case of n2 = 1.7. From FIG. 16, T = 2.9, W = 4, and D = 3.2. The horizontal axis represents position coordinates (Q) where light emitted from a point on the image display surface enters the virtual surface 308, and the vertical axis represents the angle (ν) emitted from the second panel 303. Four cases of 0, W / 4, W / 2, and 3W / 4 are shown as points on the image display surface (distance δ from the lens center line 307). δ = 3W / 4 is light from a point on the image display surface corresponding to the adjacent cylindrical lens.

  The following can be understood from FIG. Light exiting from the lens center (δ = 0) on the image display surface becomes substantially parallel light with an exit angle of approximately ν = 0. The curve representing the substantially parallel light is horizontal and higher in parallelism than in the second embodiment (hyperbola). The light emitted from the W / 4 point (δ = W / 4) from the lens center line of the image display surface is non-parallel light when entering the left end of the lens surface, but entering other lens surfaces. Becomes substantially parallel light having an emission angle near ν = 0.33. The curve representing the substantially parallel light is also horizontal and higher in parallelism than the second embodiment (hyperbola).

  Images from many viewpoints are displayed on the image display surface 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, the smallest exit angle of the light exiting from the boundary between adjacent cylindrical lenses and exiting from the panel with a relatively high intensity determines the viewing angle. In FIG. 17, the viewing angle is ± 0.62 radians (± 36 degrees). It can be seen that the viewing angle can be expanded by making the lens shape a hyperbola.

It can be seen that the lens shape that can be approximated by the fourth-order even number improves the parallelism of the emitted light, compared to the lens shape that can be approximated by a hyperbola. If the panel is observed from a certain direction, only an image in a narrower range of the image display surface is seen. That is, crosstalk is reduced.
(Embodiment 4)

Embodiment 4 shows another method for improving the parallelism of emitted light. In the hyperbolic lens, as shown in FIGS. 12 and 14, the emitted light tends to be slightly expanded. This suggests that the parallelism of the emitted light can be improved by slightly increasing the distance between the image display surface and the lower cylindrical lens without changing the hyperbolic lens shape. In Embodiment 4, (Formula 57) and (Formula 58) are used as the lens shape, and in FIG. 3, n1 = 1.5, n2 = 1.62, R = 1, m = 4, T = 5.4, It is assumed that D = 4.8 and W = 5. These satisfy (Equation 60). However, (Equation 43) and (Equation 44) are not satisfied and T is a little large. FIG. 18 shows the result of simulation using (Expression 16) to (Expression 27). The parallelism of light emitted from the lens center (δ = 0) of the image display surface and light emitted from a point (δ = W / 4) on the image display surface at a distance W / 4 from the lens center line is improved. I understand. If the panel is observed from a certain direction, only an image in a narrower range of the image display surface is seen. That is, crosstalk is reduced. The viewing angle is slightly smaller than that of the second embodiment and is ± 0.44 radians (± 25 degrees).
(Embodiment 5)

  Embodiment 5 shows a method for switching between a planar image and a stereoscopic image. Liquid crystal is filled between the cylindrical lens surfaces 302 and 304 of FIG. The liquid crystal characteristics will be described with reference to FIGS. The refractive index varies depending on the alignment direction of liquid crystal molecules and the polarization direction of light. Arrow P represents the polarization direction of light. In general, the refractive index (n2) is high when the long axes of liquid crystal molecules are aligned in parallel with the polarization method as shown in FIG. The refractive index (n1) is low. In FIG. 20, the major axis of the liquid crystal molecules is perpendicular to the paper surface.

  A method for displaying a planar image and a stereoscopic image will be described with reference to FIG. In FIG. 21, the same components as those in FIG. The major axis of the liquid crystal molecules is aligned parallel to the longitudinal direction of the cylindrical lens. The liquid crystal molecules in FIG. 21 are perpendicular to the paper surface.

  In the case of stereoscopic image display, light (A) whose polarization direction is perpendicular to the paper surface is emitted from the image display surface 306. A method of changing the polarization direction of the light emitted from the image display surface is described in FIGS. When the polarization direction is A, a state as shown in FIG. 19 occurs, and the refractive index of the liquid crystal has a large value (n2). The refractive index (n2) of the liquid crystal part is larger than the refractive index (n1) of the panels 301 and 303, and the liquid crystal part works like a lens and produces a lenticular lens effect, so that a stereoscopic image can be observed.

  In the case of flat image display, light (B) whose polarization direction is parallel to the paper surface is emitted from the image display surface 306. When the polarization direction is B, the state as shown in FIG. 20 occurs, and the refractive index of the liquid crystal has a small value (n1). If the refractive indexes of the panels 301 and 303 and the lower liquid crystal refractive index are selected to be substantially the same, the light emitted from the image display surface 306 is transmitted without being refracted in the liquid crystal portion, and a planar image can be observed. In the fifth embodiment, liquid crystal is used as the material exhibiting anisotropy, but other materials may be used as long as the refractive index varies depending on the polarization direction of light.

Alternatively, a material exhibiting an electro-optic effect in which the refractive index changes electrically is filled between the cylindrical lens surfaces 302 and 304 in FIG. Liquid crystals also exhibit this property. The polarization direction of the light emitted from the image display surface 306 is constant, and the refractive index of the biconvex cylindrical lens 305 is changed by controlling the direction of the major axis direction of the liquid crystal molecules by voltage.
(Embodiment 6)

  The specific Example using the lens shape and panel structure of Embodiment 4 of this invention is shown. A liquid crystal display having a vertical length of 1050 pixels and a horizontal length of 1400 pixels is used as the image display unit. The size of each pixel is a square having a side of 80 μm, and each pixel has a configuration in which three vertically long issuing units emitting red (R), green (G), and blue (B) are arranged.

  FIG. 22 shows a cross-sectional view of the image display device. In FIG. 22, the same components as those in FIG. One cylindrical lens is arranged in six pixel rows. That is, the width W of the cylindrical lens is 480 μm. In the fourth embodiment, the numerical values normalized by setting the radius of curvature near the lens center line 307 to R = 1 are shown. In this embodiment, since W is a reference, R = 96 μm. The thickness from the image display surface 306 to the bottom of the cylindrical lens surface 302 is T = 518 μm, and the maximum thickness of the biconvex cylindrical lens 305 is D = 461 μm. The liquid crystal forming the biconvex cylindrical lens 305 has a refractive index varying between 1.5 and 1.62, and the refractive index of the medium of the panels 301 and 303 is n = 1.5.

  FIG. 23 shows a pixel configuration of the display. In FIG. 23, reference numeral 2301 denotes a red issuer, 2302 denotes a green issuer, and 2303 denotes a blue issuer. The three issuers 2301 to 2303 form one set to constitute one pixel. One cylindrical lens is arranged for six pixel columns. Reference numeral 2304 schematically shows the cylindrical lens.

The relationship between crosstalk and pixels will be described. The sixth embodiment has the configuration of the fourth embodiment, has six columns of pixels in one cylindrical lens, and has a viewing angle of ± 0.44 radians (± 25 degrees). Accordingly, the emission angle per pixel is about 0.15 radians. As can be seen from FIG. 18, the change in the emission angle of light emitted from each point on the image display surface is within 0.15 radians, the crosstalk is within one pixel, and there is almost no crosstalk.
(Embodiment 7)

  Images from many viewpoints are displayed on the image display surface. Adjacent images on the image display surface corresponding to one cylindrical lens have a strong correlation with each other, and even if mixed, it does not cause a big problem in 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, an image having a low correlation can be prevented from being mixed and the viewing angle can be increased. This will be described using the lens shape and panel structure of the fourth embodiment. FIG. 24 shows simulation results with n1 = 1.5, n2 = 1.62, R = 1, T = 5.4, W = 5, and D = 4.8. Reference numeral 2401 denotes light emitted from a point on the image display surface at δ = 0.44 W from the lens center line, and 2402 denotes light emitted from a point on the image display surface at δ = 0.56 W. δ = 0.56W is a point on the image display surface of the adjacent cylindrical lens. The main part of the emitted light from these two points is not mixed, the maximum emission angle from δ = 0.44 W is about 0.49 radians, and the viewing angle is ± 0.49 radians (± 28 degrees). Become. The viewing angle when an image is displayed near the boundary between adjacent cylindrical lenses is ± 0.44 radians (± 25 degrees) as described above, and the viewing angle can be expanded by not displaying an image at the boundary. I understand.

FIG. 25 shows a cross-sectional view of an image display apparatus according to Embodiment 7 of the present invention. In FIG. 25, the same components as those in FIG. Reference numeral 2500 denotes a displayed image. In the case of stereoscopic image display, the refractive index of the biconvex cylindrical lens array 305 is increased, and an image is displayed only on 88% of the image display surface 306, and no image is displayed near the boundary between adjacent cylindrical lenses. In the case of flat image display, the refractive index of the biconvex cylindrical lens array 305 is reduced and an image is displayed on the entire image display surface 306.
(Embodiment 8)

In general photographs and displays, it may be difficult to see the image due to light reflection on the surface, so we want to reduce the reflection on the surface. In the conventional lenticular lens as shown in FIG. 28, the lens shape appears on the surface, and it is difficult to provide an antireflection function. In the image display devices and image printed materials of Embodiments 1 to 7 of the present invention, the surface is a flat surface and it is relatively easy to prevent reflection. FIG. 26 is a cross-sectional view of an image display object according to the eighth embodiment of the present invention. In FIG. 26, the same components as those in FIG. Reference numeral 2600 denotes the surface of an image display device or image printed material. The surface 2600 is provided with an antireflection function. For example, minute unevenness is provided on the surface 2600 to diffusely reflect the reflected light. Alternatively, a multilayer optical thin film is formed on the surface 2600 to reduce reflected light.
(Embodiment 9)

  When displaying a flat image, the resolution is high and small characters can be read. However, when displaying a stereoscopic image, the resolution is low and it is difficult to read small characters. However, I want to display small characters such as subtitles in 3D movies in foreign languages. Therefore, a part that always displays a planar image is provided in a part of the image display device. Other portions can switch between a stereoscopic image and a planar image as in the first to eighth embodiments of the present invention, or always display a stereoscopic image.

  FIG. 27 shows an example in which a portion that always displays a planar image is installed at the bottom of the screen. In FIG. 27, reference numeral 2701 denotes an image display device, and reference numeral 2702 denotes a portion where a stereoscopic image and a planar image can be switched, or a portion which always displays a stereoscopic image. Reference numeral 2703 denotes a portion that always displays a flat image, and displays subtitles and the like.

  Embodiments 1 to 9 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 defined not only by the above-described embodiments but also by the scope of claims for patent, and includes all modifications within the meaning and scope equivalent to the scope of claims for patent.

The image display device of the present invention has a function of switching between a stereoscopic image and a planar image, and the stereoscopic image has a wide viewing angle and is useful as a stereoscopic television. It can also be applied to applications such as mobile devices, personal computer monitors, and game consoles.
The three-dimensional image printed matter of the present invention has a smooth surface and a wide viewing angle, and is useful as a three-dimensional photograph or a three-dimensional picture book.

Claims (1)

It has an image display part or image printing part,
An array of first concave cylindrical lenses is formed on one side and a first concave lens array having a refractive index of n1 on the other side;
An array of second concave cylindrical lenses is formed on one side and a second concave lens array having a refractive index n1 on the other side;
The shape of the first concave cylindrical lens and the shape of the second concave cylindrical lens are the same,
The plane side of the first concave lens array is placed facing the image display unit or the image printing unit,
The second concave cylindrical lens of the second concave lens array is opposed to the first concave cylindrical lens, and the lens center line of the second concave cylindrical lens is aligned with the lens center line of the first concave cylindrical lens. Place and
A material having an anisotropy having a larger refractive index and a smaller refractive index and an anisotropy of which the smaller refractive index is approximately equal to n1 is provided between the first concave cylindrical lens and the second concave cylindrical lens. ,
Alternatively, a substance having a refractive index greater than n1 is provided between the first concave cylindrical lens and the second concave cylindrical lens.
The distance from the image display unit or the image printing unit to the bottom of the first concave cylindrical lens is T, the radius of curvature near the lens center line of the first concave cylindrical lens is R, and the distance from the lens center line is X. When the width of the first concave cylindrical lens is W,
The shape of the first concave cylindrical lens is a first function T + X ² / [R + (R ² −kX ² ) ^1/2 ]:
Alternatively, the shape of the first concave cylindrical lens is a second function of the following formula: T− [1 / {12R (ρW) ² }] · X ⁴ + [1 / (2R)] · X ²
Represented by
When represented by the first function, −0.5 <k <0.5,
When represented by the second function, ρ> 0.2
An image display object characterized by being.

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