CN1950744A - Three-dimensional display - Google Patents

Abstract

The invention provides a three-dimensional display capable of solving the problems of uneven color and uneven intensity of a three-dimensional imageAll the above steps are carried out. The three-dimensional display includes: a two-dimensional display device having a plurality of color pixels arranged in rows extending in a horizontal direction and columns extending in a vertical direction substantially perpendicular to the horizontal direction, wherein red, green, and blue color pixels are periodically arranged in the rows, and the color pixels in the columns are formed in the same color; and a microlens sheet provided on the two-dimensional display, the microlens sheet having a plurality of cylindrical lenses extending in parallel to each other, the color pixels being viewed through the cylindrical lenses, the central axes of the cylindrical lenses being inclined at an angle θ with respect to the vertical columns of the two-dimensional display, and the three-dimensional display being configured such that the pitch of the color pixels in the horizontal direction is p_xThe pitch of the color pixels in the vertical direction being p_yWhen the color pixel group forming one three-dimensional pixel is formed by 3M color pixels, namely 3M × N color pixels, where the horizontal row of one cylindrical lens is 3M and the vertical column of one cylindrical lens is N, the color pixel group has theta-tan^－1 (3p_x/Np_y) The relational expression (c) of (c).

Description

3D display

technical field

The present invention relates to a three-dimensional image display method, in particular to a three-dimensional image display using a lenticular sheet.

Background technique

At present, the display method of the three-dimensional display is a binocular stereoscopic display method as the mainstream. It is based on the principle that different images are displayed in the left and right eyes, so that people can obtain a three-dimensional effect. In the binocular stereoscopic display method, there is a disadvantage that the observation direction of an object does not change when a person moves his head, that is, there is no motion parallax. In addition, the focusing of the eyes, that is, the focusing falls on the screen on which the image is displayed, which is inconsistent with the display position of the three-dimensional object. This contradiction is the cause of eye fatigue when viewing a three-dimensional image.

Three-dimensional displays are required to perform three-dimensional display more naturally. This can be achieved by simultaneously displaying multiple images in different horizontal directions. In the multi-eye stereoscopic display method, a plurality of viewpoints are set in the horizontal direction of space, and different images are displayed at each viewpoint. By making the distance between the viewpoints smaller than the distance between the two eyes, different images are displayed for the left and right eyes. When the number of viewpoints is increased, the image seen when moving the head changes, and motion parallax can be obtained.

Recently, people have proposed the following method: Instead of setting the viewpoint in space, prepare parallel projection images of multiple three-dimensional objects, that is, directional images, for different projection directions, and display them simultaneously with quasi-parallel light in the corresponding directions (for example, See Non-Patent Document 1). It is also disclosed that natural motion parallax can be obtained when increasing the directional images to be displayed. In particular, when the number of orientation images is 64, the eyes can be focused on the 3D image, and eye fatigue when observing the 3D image can be solved (for example, refer to Non-Patent Document 2).

As described above, in a three-dimensional display, it is necessary to display a plurality of images in the horizontal direction. The horizontally/vertically arranged pixels constituting the display surface of a three-dimensional display have multiple horizontal display directions, and it is necessary to be able to control the intensity and color of light displayed in each horizontal direction. Call it a voxel.

As a method of constructing a three-dimensional display having a plurality of display directions in the horizontal direction, a method of combining a lenticular sheet with a two-dimensional display such as a liquid crystal panel is known. Here, a microlens sheet is a sheet in which a plurality of one-dimensional lenses, that is, cylindrical lenses, are arranged in a direction perpendicular to the central axis of the lenses. The cylindrical lenses constituting the lenticular sheet are arranged such that their focal planes coincide with the display surface of the liquid crystal panel. A display surface of a two-dimensional display is composed of a plurality of pixels arranged horizontally/vertically, and a single cylindrical lens corresponds to a plurality of pixels arranged in the horizontal direction to form a three-dimensional pixel. The horizontal travel direction of the light emitted from the pixel after passing through the cylindrical lens is determined by the horizontal distance from the central axis of the cylindrical lens to each pixel. Thus, the same horizontal display orientation is obtained as the number of horizontal pixels used. In this configuration method, when the number of horizontal display directions is increased, the resolution in the horizontal direction of the three-dimensional display is extremely reduced, and the problem of an unbalanced horizontal/vertical resolution in the three-dimensional display occurs.

A method for solving this problem has been proposed (see Patent Document 1). FIG. 1A is a diagram showing a structure in which a microlens sheet is obliquely arranged with respect to a vertical arrangement direction of pixels in the prior art. In FIG. 1A, a configuration method for realizing color display is illustrated, and the pixels in the figure are RGB color pixels. A three-dimensional pixel is formed by M pixels in the horizontal direction and N pixels in the vertical direction, that is, M×N color pixels, and M×N horizontal display directions are realized. At this time, when the inclination angle of the microlens sheet is θ, according to θ=tan ^-1 (p _x / _Npy ), the horizontal distance relative to the central axes of the cylindrical lenses of all the color pixels in the three-dimensional pixel can be set as set to different values. Here, p _x is the horizontal pitch of color pixels (pitch), and p _y is the vertical pitch of color pixels.

The prior art shown in FIG. 1A discloses the following contents: assuming N=2, M=7/2, 7 color pixels are used to form a three-dimensional pixel, and 7 horizontal display directions are realized. In this way, by obliquely using the microlens sheet 3, not only the color pixels 2 in the horizontal direction, but also the color pixels 2 in the vertical direction can be used to form a three-dimensional pixel, and the reduction of the horizontal resolution of the three-dimensional display can be suppressed. And can improve the balance of horizontal/vertical resolution.

Non-Patent Document 1: Yasuhiro Takagi, "Three-dimensional display using multiple telecentric optical systems with anamorphic two-dimensional arrangement", Journal of Society for Imaging Information Media, Vol.57, no.2, p294-300 (2003)

Non-Patent Document 2: Takefumi Fukutomi, Hisaka Naite, Yasuhiro Takagi, "Accommodative Responses in Three-dimensional Images Using High-Density Display of Directional Images", Journal of the Society for Imaging and Information Media, Vol.58, no.1, p69-74 (2004)

Patent Document 1: US Patent No. 6,064,424

Contents of the invention

However, in the display method disclosed in FIG. 1A, since one color pixel corresponds to one horizontal display direction, a three-dimensional pixel can only display one color of RGB three primary colors in one horizontal display direction. In particular, in FIG. 1B , the display color of the fourth horizontal display direction among the seven horizontal display directions is shown. Therefore, as shown in FIG. 1B , a method has been proposed in which full-color display is realized by using three voxels in combination.

When a person observes the screen of a three-dimensional display, as shown in FIG. 2 , light from multiple horizontal directions is incident on the eyes. In the display method disclosed in Patent Document 1, a problem has been pointed out that color unevenness occurs in a three-dimensional image due to changes in display colors of three-dimensional pixels in the horizontal display direction. Furthermore, since the maximum intensity varies with respect to the horizontal display direction depending on the pixel structure of the color pixels, there is also a problem that intensity unevenness in the horizontal direction occurs in the retinal image.

As described above, in the hitherto known display methods, only one of the three primary colors can be displayed, and it is impossible to display RGB full colors in one voxel. Furthermore, there is also a problem that color unevenness or intensity unevenness occurs in a three-dimensional image due to variations in light intensity in the horizontal display direction due to the pixel structure.

Moreover, in the prior art, the shape of the color pixel of the two-dimensional display represented by the liquid crystal display is made into a rectangle, and recently, in order to achieve the purpose of expanding the viewing angle, etc., a deformed shape such as a multi-domain shape is used. Therefore, the color pixel shape of a two-dimensional display is not limited to having a color pixel shape suitable for a three-dimensional display. Therefore, it is desired to be able to use a display panel developed as a two-dimensional display in a three-dimensional display.

In view of the above circumstances, the present inventors have made painstaking research and development in order to solve the above technical problems, and finally completed the present invention. That is, in the first embodiment of the present invention, there is provided a three-dimensional display including: a two-dimensional display having horizontal rows extending in the horizontal direction and vertical rows extending in the vertical direction substantially perpendicular to the horizontal direction. A plurality of color pixels in a column, red, green, and blue color pixels are periodically arranged on the above-mentioned horizontal row, and the color pixels in the above-mentioned column are formed in the same color; and the microlens sheet is arranged on the above-mentioned two-dimensional display , and have a plurality of cylindrical lenses extending parallel to each other, the color pixels are observed through the cylindrical lenses, the central axis of the cylindrical lenses is inclined at an angle θ with respect to the columns of the two-dimensional display, the For a three-dimensional display, when the horizontal distance between the above-mentioned color pixels is p _x , and the vertical distance between the color pixels is p _y , a color pixel group of three-dimensional pixels is formed, and the horizontal row of the above-mentioned one cylindrical lens When there are 3M, and the column of the above-mentioned one cylindrical lens is composed of N, ie, 3M×N, the above-mentioned color pixels, there is a relational expression of θ=tan ^-1 (3p _x /Np _y ). According to the above structure, in the three-dimensional display of the present invention, using a two-dimensional display in which color pixels are arranged in stripes, three kinds of color pixels can completely correspond to one horizontal display direction of light from three-dimensional pixels.

According to a preferred embodiment of the present invention, it is characterized in that the above-mentioned three-dimensional display includes color pixels of a liquid crystal display, an organic EL display, or a plasma display.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the above-mentioned N is a multiple of 3. According to the above structure, it is possible to achieve elimination of color unevenness in the horizontal display direction of the light from the voxel.

According to a preferred embodiment of the present invention, it is characterized in that, in the above three-dimensional display, Np _y ≤ 3Mp _x .

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, assuming that the horizontal width and vertical width of the color pixel are respectively w and h, then w=3p _x /N. According to the above configuration, it is possible to eliminate the intensity unevenness in the horizontal display direction of the light from the voxels.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the value of the above-mentioned w is [1-(1/2)(h/ _py )](3p _x /N)～[1+(h /p _y )](3p _x /N).

According to a preferred embodiment of the present invention, in the above three-dimensional display, the value of h is the same or similar to w. According to the above structure, variation in light intensity in the horizontal display direction of light from the voxels can be reduced.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, when the distribution of the maximum light intensity emitted from the above-mentioned color pixels is a function f(s, t), parallel to the central axis of the above-mentioned cylindrical lens, When the straight line whose horizontal distance is x from the above-mentioned central axis is represented by s=-t tanθ+x, the sum of the light intensity in a color pixel on the above-mentioned straight line is given by

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$

express,

The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; ip</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>$

φ＝tan ^-1 (x/f)

Given, where f is the focal length of the cylindrical lens,

Each parameter is set so that the above-mentioned formula (I) has a substantially constant value regardless of x.

In addition, in a second embodiment of the present invention, there is provided a three-dimensional display including: a two-dimensional display having horizontal rows extending in the horizontal direction and columns extending in the vertical direction substantially perpendicular to the horizontal direction. A plurality of color pixels, red, green, and blue color pixels are periodically arranged on the above-mentioned column; and a microlens sheet is arranged on the above-mentioned two-dimensional display, and has a plurality of cylindrical surfaces extending parallel to each other lens, the above-mentioned colored pixels are observed through the cylindrical lens, and the central axis of the above-mentioned cylindrical lens is inclined at an angle θ with respect to the columns of the above-mentioned two-dimensional display. The pitch of the color pixels is p _x , and the vertical pitch of the color pixels is p _y , forming a color pixel group of three-dimensional pixels, consisting of 3M horizontal rows of the above-mentioned cylindrical lens and 3M columns of the above-mentioned cylindrical lens When it is composed of N, that is, 3M×N, the above-mentioned color pixels, there is a relational expression of θ=tan ^-1 [(1-3/N)p _x / _py ]. According to the above structure, in the three-dimensional display of the present invention, using a two-dimensional display in which color pixels are obliquely arranged, three kinds of color pixels can completely correspond to one horizontal display direction of light from the three-dimensional pixels.

According to a preferred embodiment of the present invention, it is characterized in that the above-mentioned three-dimensional display includes color pixels of a liquid crystal display, an organic EL display, or a plasma display.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the above-mentioned N is a multiple of 3. According to the above structure, it is possible to achieve elimination of color unevenness in the horizontal display direction of the light from the voxel.

According to a preferred embodiment of the present invention, it is characterized in that, in the above three-dimensional display, Np _y ≤ 3Mp _x .

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, assuming that the horizontal width and vertical width of the color pixel are respectively w and h, then w=3p _x /N. According to the above configuration, it is possible to eliminate intensity unevenness in the horizontal display direction of the light from the voxels.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the value of the above-mentioned w is {1-(1/2)(N/3-1)(h/ _py )}(3p _x /N )≤w≤{1+(N/3-1)(h/ _py )}(3p _x /N), according to the above structure, the light intensity in the horizontal display direction of the light from the voxel can be reduced The change.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the value of the above-mentioned h is 3p _y /(N-3).

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the distribution of the maximum light intensity emitted from the above-mentioned color pixels is a function f(s, t), parallel to the central axis of the above-mentioned cylindrical lens, and The horizontal distance of the above-mentioned central axis is a straight line of x, when expressed by s=-t tanθ+x, the sum of the light intensity in a pixel on the above-mentioned straight line is given by

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$

express,

The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; II</span>}<span\; class="notranslate">\; )</span>$

φ＝tan ^-1 (x/f)

Given, where f is the focal length of the cylindrical lens,

Each parameter is set so that the above-mentioned formula (II) becomes a substantially constant value regardless of x.

Furthermore, in a third embodiment of the present invention, there is provided a three-dimensional display including: a two-dimensional display having horizontal rows extending in the horizontal direction and columns extending in the vertical direction substantially perpendicular to the horizontal direction. A plurality of color pixels, red, green, and blue color pixels are periodically arranged on the above-mentioned horizontal rows, and the color pixels in the above-mentioned columns are formed in the same color; the microlens sheet is arranged on the above-mentioned two-dimensional display, and have a plurality of cylindrical lenses extending parallel to each other, through which the colored pixels are observed; and an array of openings, arranged between the above-mentioned two-dimensional display and the above-mentioned microlens sheet, having a plurality of openings The central axis of the above-mentioned cylindrical lens is inclined at an angle of θ with respect to the columns of the above-mentioned two-dimensional display. In the three-dimensional display, when the horizontal pitch of the above-mentioned color pixels is p _x , the vertical pitch of the above-mentioned color pixels is p _y , the horizontal pitch of the above-mentioned openings is p _x ', the vertical pitch of the above-mentioned openings is p _y ', a color pixel group of a three-dimensional pixel is formed, and the horizontal row of the above-mentioned one cylindrical lens When being 3M, the column of above-mentioned one cylindrical lens is N, i.e. 3M*N above-mentioned color pixel constitutes, p _x =p _x ', p _y = _py ', have θ=tan ^-1 (3p _x '/Np _y ') relationship. In the third embodiment of the present invention, by using an aperture array in a predetermined relationship with respect to the shape of color pixels, it is possible to suppress divergence of light emitted from color pixels of a two-dimensional display and generate optimal color pixels.

According to a preferred embodiment of the present invention, it is characterized in that the above-mentioned three-dimensional display includes color pixels of a liquid crystal display, an organic EL display, or a plasma display.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the above-mentioned N is a multiple of 3.

According to a preferred embodiment of the present invention, it is characterized in that, in the above three-dimensional display, Np _y '≤3Mp _x '.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, assuming that the horizontal width and vertical width of the opening are respectively w' and h', then w'=3p _x '/N.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the value of the above-mentioned w' is 1-(1/2)(h'/ _py ′)(3p _x ′/N)～ The range of 1+(h′/ _py ′)(3p _x ′/N).

According to a preferred embodiment of the present invention, it is characterized in that, in the above three-dimensional display, the value of h' is the same or similar to p _y '.

According to a preferred embodiment of the present invention, it is characterized in that in the above-mentioned three-dimensional display, the distribution of the maximum light intensity emitted from the above-mentioned opening is a function f(s, t), which is parallel to the central axis of the above-mentioned cylindrical lens and parallel to the above-mentioned The horizontal distance of the central axis is a straight line of x, when expressed by s=-ttanθ+x, the sum of the light intensity in a color pixel on the above-mentioned straight line is given by

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$

express,

The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; an</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; III</span>}<span\; class="notranslate">\; )</span>$

φ＝tan ^-1 (x/f)

Given, where f is the focal length of the cylindrical lens,

Each parameter is set so that the above-mentioned formula (III) becomes a substantially constant value regardless of x.

According to a preferred embodiment of the present invention, in the above-mentioned three-dimensional display, the color pixel has a plurality of regions divided into up, down, left, and right.

According to a preferred embodiment of the present invention, it is characterized in that the above-mentioned three-dimensional display further includes a diffusion plate arranged between the above-mentioned two-dimensional display and the above-mentioned opening array.

Furthermore, in a fourth embodiment of the present invention, there is provided a three-dimensional display including: a two-dimensional display having horizontal rows extending in the horizontal direction and columns extending in the vertical direction substantially perpendicular to the horizontal direction. A plurality of color pixels, red, green, and blue color pixels are periodically arranged on the above-mentioned columns; a microlens sheet is arranged on the above-mentioned two-dimensional display, and has a plurality of cylindrical lenses extending parallel to each other , the color pixels are observed through the cylindrical lens; and the opening array is arranged between the above-mentioned two-dimensional display and the above-mentioned microlens sheet, and has a plurality of openings; the central axis of the above-mentioned cylindrical lens is relative to the above-mentioned The columns of the two-dimensional display are inclined at an angle of θ. In the three-dimensional display, if the horizontal pitch of the above-mentioned color pixels is p _x , the vertical pitch of the above-mentioned color pixels is p _y , and the horizontal pitch of the above-mentioned opening is The pitch is p _x ', and the pitch in the vertical direction of the above-mentioned opening is p _y ', which constitutes a color pixel group of three-dimensional pixels. When being listed as N, i.e. 3M×N above-mentioned colored pixels, p _x =p _x ', p _y = _py ', have θ=tan ^-1 [(1-3/N)p _x '/p _y '] relational expression. In the fourth embodiment of the present invention, by using an aperture array in a predetermined relationship with respect to the shape of the color pixels, it is possible to suppress the divergence of light emitted from the color pixels of the two-dimensional display and generate optimal color pixels.

According to a preferred embodiment of the present invention, it is characterized in that the above-mentioned three-dimensional display includes color pixels of a liquid crystal display, an organic EL display, or a plasma display.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the above-mentioned N is a multiple of 3.

According to a preferred embodiment of the present invention, it is characterized in that, in the above three-dimensional display, N _y '≤3Mp _x '.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, assuming that the horizontal width and vertical width of the opening are respectively w' and h', then w'=3p _x '/N.

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the value of the above-mentioned w' is {1-(1/2)(N/3-1)(h/py _′ )}(3p _x '/N)≤w'≤{1+(N/3-1)(h/p _y ')}(3p _x '/N).

According to a preferred embodiment of the present invention, it is characterized in that, in the above-mentioned three-dimensional display, the value of the above-mentioned h' is 3p _y '/(N-3).

According to a preferred embodiment of the present invention, it is characterized in that in the above-mentioned three-dimensional display, the distribution of the maximum light intensity emitted from the above-mentioned opening is a function f(s, t), which is parallel to the central axis of the above-mentioned cylindrical lens and parallel to the above-mentioned The horizontal distance of the central axis is a straight line of x, when expressed by s=-ttanθ+x, the sum of the light intensity in a color pixel on the above-mentioned straight line is given by

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$

express,

The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; IV</span>}<span\; class="notranslate">\; )</span>$

φ＝tan ^-1 (x/f)

Given, where f is the focal length of the cylindrical lens,

Each parameter is set so that the above-mentioned formula (IV) becomes a substantially constant value regardless of x.

According to a preferred embodiment of the present invention, in the above-mentioned three-dimensional display, the color pixel has a plurality of regions divided into up, down, left, and right.

According to a preferred embodiment of the present invention, it is characterized in that the above-mentioned three-dimensional display further includes a diffusion plate arranged between the above-mentioned two-dimensional display and the above-mentioned opening array.

According to the present invention, a plurality of different images can be displayed in the horizontal display direction, realizing a three-dimensional display in which color unevenness and intensity unevenness are eliminated.

Description of drawings

FIG. 1A is a plan view schematically showing the relationship between a two-dimensional display and a lenticular sheet in a prior art color display based on a three-dimensional display. Fig. 1B shows the color of voxels displayed in a specific horizontal direction.

2 is a horizontal cross-sectional view schematically showing the relationship between the horizontal display direction and the retinal image in three-dimensional display.

Fig. 3 is a diagram schematically showing the structure of a voxel in the first embodiment of the present invention.

Fig. 4A is a diagram for explaining the horizontal display direction [phi] of light rays emitted from voxels. FIG. 4B is an enlarged view of a part of the plane 21 shown in FIG. 4A .

Fig. 5 is a diagram showing the relationship between color pixels of the same color and cylindrical lenses in the first embodiment of the present invention.

Fig. 6 shows the relationship between the horizontal display direction and the maximum light intensity when the shape of the color pixel is rectangular in the present invention. Figure 6A shows the case of h tanθ≤w, and Figure 6B shows the case of h tanθ≥w.

7A and 7B are diagrams showing conditions under which the maximum light intensity in the horizontal display direction for one voxel becomes constant in the present invention. Here, as shown in FIG. 7A , the maximum light intensity does not change along the horizontal display direction, which is the condition that the trapezoidal hypotenuse representing the intensity distribution for one color pixel completely overlaps with the opposite trapezoidal hypotenuse.

8A, 8B, 8C, and 8D are graphs showing the conditions under which the light intensity change in the horizontal display direction for one voxel is 50%.

Fig. 9 is a diagram schematically showing the structure of a voxel when N=6 in one embodiment of the first embodiment of the present invention.

Fig. 10 is a diagram schematically showing the structure of voxels when N=4 in one embodiment of the first embodiment of the present invention.

FIG. 11A is a graph showing the maximum light intensity of the emitted light quantity distribution for a pixel of an arbitrary shape, and FIG. 11B is a graph showing the maximum light intensity in the horizontal display direction for a pixel of an arbitrary shape.

Fig. 12 is a graph showing the light intensity in the horizontal display direction with respect to a voxel using arbitrary shape color pixels in the present invention.

Fig. 13 is a diagram showing the relationship between the arrangement of oblique color pixels and the horizontal distance from the central axis of the cylindrical lens to the center of the color pixels in the second embodiment of the present invention.

Fig. 14 shows the structure of voxels when N=6 in one embodiment of the second embodiment of the present invention.

Fig. 15 shows the structure of voxels when N=4 in one embodiment of the second embodiment of the present invention.

Fig. 16 is a schematic cross-sectional view of a three-dimensional display according to third and fourth embodiments of the present invention.

FIG. 17 is a diagram illustrating the relationship between the two-dimensional display and the aperture array in the third and fourth embodiments of the present invention. The hatching in FIG. 17 indicates the light shielding portion.

Fig. 18 is a schematic cross-sectional view showing an example of a color pixel structure used in a two-dimensional display of the present invention. RGB in FIG. 18 has color pixels of the same color in the vertical direction.

19 is a schematic cross-sectional view of a three-dimensional display provided with a diffusion plate among three-dimensional displays according to third and fourth embodiments of the present invention.

Fig. 20 shows a schematic diagram of a color pixel structure used in an embodiment of the present invention. RGB in FIG. 13 has color pixels of the same color in the vertical direction.

FIG. 21A shows a part of the intensity distribution in the horizontal display direction for a color pixel in an embodiment of the present invention, and FIG. 21B shows a part of the intensity distribution in the horizontal display direction for a three-dimensional pixel in an embodiment of the present invention.

FIG. 22 shows the specifications of a three-dimensional display designed to be N=6 in the present invention.

Fig. 23 is a picture showing a three-dimensional image obtained by using a three-dimensional display trial-manufactured according to the type I specification of the present invention.

Detailed ways

Embodiments of the present invention will be described with reference to the drawings. The following embodiments are examples for explaining the present invention, and the present invention is not limited to the embodiments. The present invention can be implemented in various forms as long as it does not deviate from the technical idea. Since the same reference numerals denote the same parts, they are commonly used for all the drawings in this specification.

A three-dimensional display of the present invention includes a two-dimensional display and a lenticular sheet disposed on the two-dimensional display.

(first embodiment of the present invention)

In the two-dimensional display used in the present invention, in order to realize color display, three kinds of color pixels corresponding to the three primary colors of RGB are two-dimensionally arranged in the vertical direction and the horizontal direction. In the first embodiment of the present invention, a stripe configuration is used for description. The stripe configuration is such that the three color pixels corresponding to the RGB three primary colors are arranged with the same color pixels in the vertical direction, and the RGB color pixels are arranged in the horizontal direction. Color pixels are periodically arranged. In the following description, three types of RGB are used as color pixels, but the concept of the present invention can also be used in cases other than three types, for example, four types.

Examples of the two-dimensional display having a color pixel structure used in the present invention include, but are not limited to, liquid crystal displays, plasma displays, and organic EL displays.

In addition, the microlens sheet used in the present invention is a sheet of cylindrical lenses having a plurality of elongated semiconical lenses, and is a sheet in which the plurality of cylindrical lenses are arranged in a direction perpendicular to the central axis of the cylindrical lenses.

In the present invention, a three-dimensional pixel is constituted by three times the number of color pixels in the horizontal display direction, and a full-color displayable three-dimensional pixel is realized.

Fig. 3 is a diagram schematically showing the voxel structure of the present invention. As mentioned above, in FIG. 3, the microlens sheet 3 used in the present invention is a sheet having a one-dimensional lens, that is, a cylindrical lens 4, and a plurality of lenses are arranged in a direction perpendicular to the central axis 8 of the cylindrical lens. . Furthermore, the microlens sheet 3 is arranged so that the focal plane of the cylindrical lens coincides with the display surface on which the color pixels 2 of the two-dimensional display 1 are arranged.

For the central axis 8 of the cylindrical lens, the light emitted from a point on the display surface of the two-dimensional display of the distance x in the horizontal direction is refracted by the cylindrical lens 4, and is expressed as an angle φ=tan ^-1 (x /f). Here, f is the focal length of the cylindrical lens, and  refers to the horizontal display direction of the light emitted from the voxel. Therefore, by using the cylindrical lens central axis 8 obliquely with respect to the vertical arrangement direction of the color pixels 2, different horizontal display directions can be given to the same color pixels 2 with different vertical positions at the same horizontal position.

4A and 4B are diagrams for explaining the horizontal display direction [phi]. As shown in FIG. 4A , on a constant plane 21 perpendicular to the display surface of the 3D display, the angle ray 22 of the light emitted from the 3D display 20 travels with respect to the normal of the display surface is called φ. FIG. 4B is an enlarged view of a part of the above-mentioned plane 21, and schematically shows the relationship between the above-mentioned x, f, and φ.

As described above, in the present invention, as shown in FIG. 3, one cylindrical lens 4 corresponds to 3M color pixels in the horizontal direction and N in the vertical direction, that is, 3M×N color pixels to form a three-dimensional pixel. In this case, the three color pixel groups of RGB will use M×N respectively. The case where M=4 and N=4 is shown in FIG. 3 .

The inclination angle θ of the central axis of the cylindrical lens with respect to the direction in which the color pixels are vertically arranged can be obtained in the following manner. That is, when considering the horizontal distance from the central axis of the cylindrical lens, among color pixels of the same color, the horizontal distance varies by p _y tanθ between the closest color pixels whose vertical positions differ by 1 pixel. When the change Np _y tanθ of the horizontal distance corresponding to the difference in the vertical position of N pixels is equal to the change 3p _x of the horizontal distance of the same color color pixel on the same horizontal line, the same color color pixel in a three-dimensional pixel The horizontal distance changes at equal intervals. Therefore, by Np _y tanθ=3p _x , the inclination angle θ of the microlens sheet is calculated as θ=tan ⁻¹ (3p _x /Np _y ).

At this time, the M×N color pixels corresponding to RGB colors have completely different horizontal distances with respect to the central axis 8 of the cylindrical lens, and their values change at equal intervals p _y tanθ=3p _x /N. Therefore, M×N horizontal display directions can be realized for each color of RGB, and the intensity and color of light displayed in each horizontal display direction can be controlled. In FIG. 3, 16 horizontal display directions are realized by using 12 color pixels in the horizontal direction and 4 pixels in the vertical direction.

As mentioned above, in the present invention, constitute a three-dimensional pixel by 3M on the horizontal direction, N on the vertical direction, i.e. 3M*N color pixels, if the inclination angle θ of the microlens sheet is θ=tan ^-1 ( 3p _x /Np _y ), so that full-color display can be performed in M×N horizontal display directions.

On the other hand, in the prior art disclosed in Patent Document 1, a three-dimensional pixel is composed of M color pixels in the horizontal direction and N color pixels in the vertical direction, that is, M×N, to realize M×N horizontal display directions. . Therefore, in one voxel, basically only one color in RGB can be displayed. Also, the inclination angle θ of the microlens sheet = tan ^-1 (p _x /Np _y ). In this way, in the display method disclosed in Patent Document 1, one horizontal display direction can only correspond to one color pixel in the RGB color pixels, but in the actual method of the present invention, for a horizontal display direction, RGB The 3 color pixels will correspond exactly.

Within a voxel, the difference in vertical positions of RGB color pixels displayed in the same horizontal direction is at most the vertical width of the voxel (Np _x ). In order for the difference in vertical position to be imperceptible and the voxel to be identified as a pixel, it is preferable that the horizontal width of the voxel (3Mp _x ) is greater than or equal to the difference in maximum vertical position ( _Npy ). That is, it is preferable that Np _y ≦3Mp _x .

Since the color pixel is not a point, it has a certain size, so the horizontal distance of a color pixel relative to the central axis of the cylindrical lens is a constant width. Therefore, the horizontal display direction occupied by one color pixel is also of constant width.

Fig. 5 is a diagram showing the relationship between color pixels of the same color and cylindrical lenses. As shown in FIG. 5, c represents the horizontal distance between the center of a color pixel 2 and the central axis 8 of the cylindrical lens. Consider a straight line parallel to the central axis 8 of the cylindrical lens at a horizontal distance x. Reference numeral 11 shown in FIG. 5 indicates a straight line parallel to the central axis of the cylindrical lens.

The light emitted from each point on the parallel line passes through the cylindrical lens, and travels in the same direction in the horizontal direction at an angle φ=tan ⁻¹ (x/f). Thus, the length of a colored pixel cut across the parallel line determines the maximum intensity of light traveling in the horizontal direction.

Next, the case where the shape of the color pixel is a rectangle will be discussed. Let the horizontal width of the rectangle be w and the vertical width be h. The relationship between the horizontal display direction  and the maximum intensity I of the light passing through the cylindrical lens is as follows.

When h tanθ≤w,

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

φ＝tan ^-1 (x/f)

When h tanθ≥w,

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; w</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; w\&theta;</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; 0</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

φ＝tan ^-1 (x/f)

Here, when I is represented by a function having the horizontal display direction  as a variable, since it is a complex functional expression including an inverse trigonometric function, the distance x from the central axis of the cylindrical lens is used as a variable.

6A and 6B are graphs showing the above results. FIG. 6A shows the case of h tanθ≦w, and FIG. 6B shows the case of h tanθ≧w. The value of the horizontal distance between the color pixel groups of the same color relative to the central axis of the cylindrical lens changes at an equal distance p _y tanθ. Therefore, the maximum light intensity in the horizontal display direction for voxels can be obtained by superimposing the intensity distributions in Figs. 6A and 6B with shifts of py _tanθ one by one in the horizontal axis direction. Here, although it is a matter of course, it is preferable that the maximum light intensity does not change along the horizontal display direction.

7A and 7B are diagrams showing conditions under which the maximum light intensity in the horizontal display direction for one voxel becomes constant. As shown in Figure 7A, the maximum light intensity in the horizontal display direction does not change, which is to satisfy the situation that the trapezoidal hypotenuse representing the intensity distribution of one color pixel completely coincides with the opposite trapezoidal hypotenuse, which is called Fig. 7B The intensity distribution shown is the case.

When this condition is h tanθ≤w, the distance between the trapezoids when the hypotenuses of the trapezoids are completely overlapped is w, so it can only be realized when w= _py tanθ is established. In other words, it can be seen from tanθ=3p _y /Np _y that it can only be realized when the horizontal width of the color pixel w=3p _x /N.

On the other hand, when h tanθ≥w, the distance between the trapezoids when the hypotenuses of the trapezoids are completely overlapped is h tanθ, which can only be realized when h tanθ=py tanθ, that is, h= _{py y .} This cannot be fully satisfied because there is a light-shielding portion between the upper and lower color pixels, and h< _py . Reducing the light-shielding part can be roughly satisfied, but according to the relationship of h tanθ≥w and tanθ=3p _y /Np _y , it is necessary to make p _x /w≥N/3. Since there is also a light-shielding portion between the left and right color pixels, it is necessary to make N less than or equal to 3 when p _x /w≤1 is considered. Therefore, the number of vertically colored pixels used by voxels is limited.

Next, the conditions for suppressing the maximum slight variation to 50% or less were obtained. Here, consider the case where h tanθ≤w. 8A and 8B are diagrams showing the conditions under which the light intensity change in the horizontal display direction for one voxel is 50%. Fig. 8A shows the situation where trapezoids overlap too much. According to wh tanθ= _py tanθ, the horizontal width w=(1+h/ _py )(3p _x /N) of the color pixel satisfying this formula is calculated. At this time, the maximum light intensity in the horizontal display direction of the voxel is as shown in FIG. 8B. Fig. 8C shows the case of insufficient trapezoidal coincidence. According to (1/2)h tanθ+w= _py tanθ, w=[1-(1/2)(h/ _py )](3p _x /N) is obtained. At this time, the maximum light intensity in the horizontal display direction of the voxel is as shown in FIG. 8D. According to the above description, in order to make the change of the light intensity in the horizontal display direction less than or equal to 50%, it is necessary to make the horizontal width of the color pixel satisfy:

{1-(1/2)(h/p _y )}(3p _x /N)≤w≤{1+(h/p _y )}(3p _x /N).

The ideal color pixel width 3p _x /N is an allowable range from 1-(1/2)(h/ _py ) times to 1+(h/py ₎ . In particular, it can be seen that the larger h/py _y is, that is, the larger the vertical width h of the color pixel, the larger the allowable range relative to the horizontal width w of the color pixel.

As is clear from the above description, when considering the manufacturing accuracy of the pixel, even in the case of w=3p _x /N, the vertical width h of the pixel is increased, preferably close to p _y .

Considering in the same way, when it is required to suppress the change of the maximum strength to less than or equal to 20%, then

{1-(1/5)(h/p _y )}(3p _x /N)≤w≤{1+(1/4)(h/p _y )}(3p _x /N).

When the horizontal width of the color pixel w=3p _x /N, the theoretical maximum light intensity does not change with the horizontal display direction. In practice, however, this requirement cannot be fully met due to reasons such as manufacturing errors. Also, when w=3p _x /N is not satisfied, of course, the maximum light intensity in the horizontal display direction changes. If the direction in which the light intensity of each color of RGB becomes the maximum/minimum does not match, color deviation occurs in the horizontal display direction, and the color reproducibility of the three-dimensional image deteriorates. For example, when white is displayed, the color changes to RGB depending on the horizontal display direction. Between color pixels of different colors, the horizontal distance relative to the central axis of the cylindrical lens is a different value of p _x or 2p _x . In the color pixels of the same color, the horizontal distance of the color pixels relative to the central axis of the cylindrical lens changes at equal intervals p _y tanθ=(3/N)p _x . When the position of the color pixel of the same color changes by N/3 pixels in the vertical direction, the horizontal distance changes by p _x , and when it changes by 2N/3 pixels, the horizontal distance changes by 2p _x . Therefore, when N is a multiple of 3, the horizontal distances of RGB color pixels can be completely consistent. Thereby, the variation of the light intensity in the horizontal display direction can be made uniform in the three primary colors of RGB, and the color deviation in the horizontal display direction can be eliminated.

w= _px when N=3. It is difficult to strictly satisfy this relationship when considering the presence of light-shielding portions between color pixels. Here, an example when N=6 is shown in FIG. 9 . In FIG. 9, the inclination angle of the microlens sheet is θ=tan ^-1 (p _x /2p _y ). In addition, when w=p _x /2, it is designed so that the maximum intensity variation in the horizontal display direction does not occur. In addition, it is designed to suppress color deviation that occurs when w=p _x /2 cannot be strictly satisfied due to manufacturing precision by taking N as a multiple of 3. In FIG. 9, when M=6, one three-dimensional pixel is constituted by 108 color pixels, and 36 horizontal display directions are realized.

Fig. 10 is a design example when N=4. In this case, the inclination angle θ of the microlens sheet is θ=tan ⁻¹ (3p _x /4p _y ). In addition, when w=3px/4, it is designed so that the variation of the maximum intensity in the horizontal display direction does not occur. In FIG. 10, when M=4, one three-dimensional pixel is constituted by 48 color pixels, and 16 horizontal display directions are realized.

In the above description, the shape of the color pixel is described as a rectangle. However, the actual shape of a color pixel is a shape in which a part of a rectangle is missing, or a pixel structure deformed into a multi-region structure is used. Here, for the case where the color pixel has an arbitrary shape, the detailed description is as follows.

Fig. 11A is a diagram showing pixels of an arbitrary shape and distribution of emitted light quantities. Fig. 11B is a graph showing the maximum light intensity occupied by one pixel with respect to the horizontal display direction. The distribution of the maximum light intensity emitted from the color pixels is represented by the function f(s, t). In FIG. 11A , a straight line parallel to the central axis of the cylindrical lens is considered on the light emitting surface of the two-dimensional display. The light emitted from the parallel line travels in the same horizontal direction after passing through the cylindrical lens. Therefore, the maximum light intensity in the corresponding horizontal display direction [phi] is obtained by using the sum of the light intensities at points on the parallel lines in the pixel. The straight line parallel to the central axis 8 of the cylindrical lens and the horizontal distance x is represented by s=-t tanθ+x, so the sum of the pixel intensity on the straight line is given by the following formula.

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$

φ＝tan ^-1 (x/f)

FIG. 11B is a diagram illustrating this case. The horizontal distance from the central axis of the cylindrical lens of the color pixels of the same color changes at equal intervals p _y tanθ. Accordingly, the light intensity in the horizontal display direction for the entire voxel is given by the following equation.

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; ip</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>$

Fig. 12 is a graph showing the light intensity in the horizontal display direction for a voxel using arbitrary shape color pixels. In FIG. 12, by superimposing the light intensity from each pixel shown by the dotted line, the light intensity in the horizontal display direction with respect to the voxel shown by the solid line is obtained. As shown in FIG. 12, it is preferable to determine the pixel structure and the inclination angle θ of the lenticular sheet so that the superimposed light intensity Is(x) indicated by the solid line is substantially constant in the horizontal display direction.

(second embodiment of the present invention)

In the above description, the case where the three color pixels corresponding to the three primary colors of RGB are arranged in stripes has been described. As an arrangement of color pixels, an oblique color pixel arrangement in which color pixels of the same color are slanted in an oblique direction is also conceivable, and the second embodiment of the present invention will be described using this arrangement.

Fig. 13 shows the relationship between the arrangement of oblique color pixels and the horizontal distance from the central axis of the cylindrical lens to the center of the color pixels in the second embodiment of the present invention. When considering color pixels of the same color, the horizontal distance varies by p _{x -py} tanθ between the closest color pixels whose vertical positions differ by 1 pixel. When the change N(p _{x -py} tanθ) of the horizontal distance corresponding to the difference in the vertical position of N pixels is equal to the change 3p _x of the horizontal distance of the same color pixel on the same horizontal line, the same color in a three-dimensional pixel The horizontal distance of the color pixels varies at equal intervals. Therefore, by N(p _{x −py} tanθ)=3p _x , the inclination angle θ of the microlens sheet is calculated as θ=tan ⁻¹ [(1-3/N)p _x /py _y )].

As described above, in the case of the stripe arrangement, the horizontal distances of the pixels of the same color are varied at equal intervals p _x tanθ, and in the oblique color pixel arrangement, are varied at equal intervals of p _{x -py} tanθ. For the inclination angle of the lenticular sheet, it is θ=tan ^-1 (3p _x / _Npy ) when it is configured for stripes, and it is θ=tan ^-1 [(1-3/N) when it is configured for inclined color pixels p _x /p _y )].

By modifying the above two points, the results obtained when the stripes are arranged can also be applied to the case where the oblique color pixels are arranged.

Here, the conditions for making the maximum intensity of the voxels in the horizontal display direction constant are obtained as follows. When the color pixels are rectangular, the light intensity in the horizontal display direction occupied by one color pixel can be displayed in the same manner as when the stripes are arranged, and has the distribution shown in FIG. 6 . However, since the horizontal distance between the color pixels of the same color and the central axis of the cylindrical lens changes at equal intervals p _{x -py} tanθ, it is necessary to consider replacing p _y in Figures 7A and 7B with p _{x -py} tanθ tanθ, it can be seen that when h tanθ≤w, it can be realized when w=p _{x -py} tanθ. Therefore, it can be seen that w=3p _x /N is sufficient. In addition, it can be seen that h tanθ≧w can be realized when h tanθ=p _{x −py} tanθ. Therefore, it can be seen that h=3p _y /(N-3) is enough.

In addition, in order to make the light intensity change in the horizontal display direction less than or equal to 50%, the horizontal width of the color pixel needs to satisfy

{1-(1/2)(N/3-1)(h/p _y )}(3p _x /N)≤w≤{1+(N/3-1)(h/p _y )}(3p _x /N).

Furthermore, in order to suppress the variation of the maximum intensity to 20% or less, the condition is

{1-(1/5)(N/3-1)(h/p _y )}(3p _x /N)≤w≤{1+(1/4)(N/3-1)(h/p _y )}(3p _x /N).

Also, the number N of color pixels in the vertical direction constituting one voxel is preferably a multiple of 3 for the same reason as in the stripe arrangement. Likewise, it is preferable that Np _y ≦3Mp _x .

In the case of an oblique color pixel arrangement based on the above description, an example of a preferred embodiment of the present invention is shown in FIG. 14 . In one of the second embodiments of the present invention shown in FIG. 14, w=p _x /2 when N=6. In the embodiment shown in FIG. 14 , the inclination angle of the lenticular sheet is θ=tan ⁻¹ (p _x /2p _y ). In addition, it is designed so that when w=p _x /2, the variation of the maximum intensity in the horizontal display direction does not occur. Moreover, it is designed to suppress color deviation due to manufacturing precision when w=p _x /2 cannot be strictly satisfied by taking N as a multiple of 3. In FIG. 14, when M=6, one three-dimensional pixel is constituted by 108 color pixels, and 36 horizontal display directions are realized.

Fig. 15 is a design example when N=4. In this case, the inclination angle θ of the microlens sheet = tan ^-1 (p _x /4p _y ). In addition, when w=3p _x /4, it is designed so that the maximum intensity variation in the horizontal display direction does not occur. In FIG. 15, when M=4, one three-dimensional pixel is constituted by 48 color pixels, and 16 horizontal display directions are realized.

In the second embodiment of the present invention, when color pixels are not rectangular but have arbitrary shapes, the same considerations as in the stripe arrangement can be considered. In the case of an arbitrary shape, since the horizontal distance between color pixels of the same color changes at equal intervals p _{x -py} tanθ, the light intensity in the horizontal display direction for the entire three-dimensional pixel is expressed by the following equation.

${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

Therefore, it is preferable to determine the pixel structure and the inclination angle of the lenticular sheet so that Is(x) is substantially constant.

In the above description, the method of tilting the lenticular sheet was described, but those skilled in the art can easily understand that the same effect can be obtained by tilting the two-dimensional display instead of tilting the lenticular sheet.

In the description of the first and second embodiments of the present invention, the construction method of the present invention was described using a microlens sheet, but those skilled in the art can easily understand that a parallax barrier can also be used (parallax barrier) to replace the microlens sheet. Here, the so-called parallax barrier means that slits are arranged in a direction perpendicular to the longitudinal direction thereof. At this time, the parallax barrier can be arranged not only on the observer side of the two-dimensional display, but also on the opposite side of the observer, that is, between the display surface of the display and the backlight.

In addition, in the above description, the description has been made using the structure in which the cylindrical lens is arranged corresponding to directly above the color pixel group constituting the voxel. That is, the description has been made using a configuration in which the horizontal pitch of the voxels is equal to the horizontal pitch of the cylindrical lenses constituting the lenticular sheet. However, the present invention is applicable even in the case where the above two pitches are not equal. This is a technique widely used to expand the horizontal viewing range of a 3D image at a specific viewing distance from a 3D screen.

(third embodiment of the present invention)

The basic configuration of the three-dimensional display according to the third embodiment of the present invention is the same as that of the first embodiment of the present invention. Thus, the relationship between the horizontal pitch and the vertical pitch of the color pixels of the two-dimensional display, the inclination angle θ of the central axis of the cylindrical lens, and the number of color pixel groups related to the horizontal row and column of the cylindrical lens The formula is the same as that of the first embodiment of the present invention.

However, the three-dimensional display 50 according to the third embodiment of the present invention has an aperture array 30 provided between the two-dimensional display 1 and the lenticular sheet 3 as shown in FIG. 16 . Here, the opening array used in the present invention may use a metal film such as a chromium mask, but is not limited thereto. Alternatively, black stripes made of light-absorbing material used for light-shielding wiring portions between color pixels in a liquid crystal display panel may be used for the opening array. In the black stripes used in the two-dimensional display, RGB color filters are formed in the openings, but the opening array used in the present invention does not require color filters. In addition, between the opening array 30 shown in FIG. 16 and the two-dimensional display, the two-dimensional display 1 is kept parallel to the above-mentioned opening array 30. In order to maintain a constant distance between the two-dimensional display 1 and the opening array 30, a glass substrate is preferably separated or plastic sheets such as polypropylene.

FIG. 17 is a diagram illustrating the relationship between the two-dimensional display 1 and the aperture array 30 used in the third embodiment of the present invention. In FIG. 17, the shape of the color pixel of the two-dimensional display 1 is described in the shape of "ㄑ", but the present invention is not limited to this shape. The horizontal and vertical pitches of the color pixels of the two-dimensional display 1 shown in FIG. 17 are p _x , p _{y ,} respectively. However, in the opening array 20 used in the third embodiment of the present invention, the horizontal and vertical pitches of the openings 20 are respectively p _x ' and p _y ', and the horizontal and vertical widths of the openings are respectively w' and h'.

In addition, when p _x , p _y , p _x ' and p _y ' satisfy the following relational expressions, the light emitted from the color pixel can pass through the aperture array to generate a virtual color pixel having an optimal shape for a three-dimensional display.

p _x = p _x ', p _y = p _y ', θ = tan ^-1 (3p _x '/Np _y ').

The meaning of the relational expression of θ=tan ^-1 (3p _x '/Np _y ') is the same as that described in the first embodiment of the present invention.

Like this, use the aperture array that has the aperture portion that conforms to above-mentioned relational expression, by making its aperture shape to be optimal shape, become the optimal shape of the color pixel of each light RGB that two-dimensional display sends out, can realize to horizontal display direction Changes in light intensity and suppression of color unevenness.

Fig. 18 shows a schematic diagram of a color pixel structure that can be used in a two-dimensional display according to a third embodiment of the present invention and a fourth embodiment described below. Here, the color pixel structure shown in FIG. 18 is divided into up, down, left, and right, and has a so-called multi-region structure. RGB has color pixels of the same color in the vertical direction. The color pixel structure concerned can also be applied to the third embodiment of the present invention and the fourth embodiment described below.

FIG. 19 is a schematic cross-sectional view of a three-dimensional display 50 in which a diffusion plate 35 is provided between the aperture array 30 and the two-dimensional display as a modification of the third embodiment of the present invention. Between the opening array 30 and the diffusion plate 35, between the two-dimensional display 1 and the above-mentioned diffusion plate 35, the parallelism of the above-mentioned diffusion plate 35 and the above-mentioned opening array relative to the two-dimensional display 1 is maintained, in order to maintain the parallelism with each component 1 , 35, and 30 have a constant distance, preferably separated by glass substrates or plastic plates such as polypropylene. The structure shown in FIG. 19 is that when the diffuseness of the light emitted from the color pixels of the two-dimensional display 1 is low and sufficient light intensity distribution cannot be obtained in the openings of the opening array 30, it can be displayed in the two-dimensional display 1. A diffuser plate is arranged between the color pixels of the display and the array of openings to adjust the diffuseness of the light.

(Fourth embodiment of the present invention)

The basic configuration of the three-dimensional display according to the fourth embodiment of the present invention is the same as that of the second embodiment of the present invention. Thus, the relationship between the horizontal pitch and the vertical pitch of the color pixels of the two-dimensional display, the inclination angle θ of the central axis of the cylindrical lens, and the number of color pixel groups related to the horizontal row and column of the cylindrical lens The formula is the same as the second embodiment of the present invention.

However, a three-dimensional display 50 according to the fourth embodiment of the present invention has an aperture array 30 provided between the two-dimensional display 1 and the lenticular sheet 3 as shown in FIG. 16 . Here, since the aperture array used in the present invention is the same as that described in the third embodiment of the present invention, description thereof will be omitted.

FIG. 17 is a diagram illustrating the relationship between the two-dimensional display 1 and the aperture array 30 used in the fourth embodiment of the present invention. In FIG. 17, the shape of the color pixel of the two-dimensional display 1 is described in the shape of "ㄑ", but the present invention is not limited to this shape. The horizontal and vertical pitches of the color pixels of the two-dimensional display 1 shown in FIG. 17 are p _x , p _{y ,} respectively. However, in the fourth embodiment of the present invention, the horizontal and vertical pitches of the openings 20 of the opening array 20 are respectively p _x ' and p _y ', and the horizontal and vertical widths of the openings are respectively w' and h'.

Moreover, when p _x , p _y , p _x ' and p _y ' satisfy the following relational expression, the light emitted from the color pixel can pass through the aperture array to generate a virtual color pixel with an optimal shape in a three-dimensional display.

p _x = p _x ', p _y = p _y ', θ = tan ^-1 [(1-3/N)p _x '/p _y '].

The meaning of the relational expression of θ=tan ^-1 [(1-3/N)p _x '/ _py '] is the same as that described in the second embodiment of the present invention.

In this way, using an aperture array having apertures conforming to the above relational expression, the optimal shape of the color pixels of each light RGB emitted by the two-dimensional display can be achieved, and the variation of light intensity in the horizontal display direction and the suppression of color unevenness can be realized. .

FIG. 19 is a schematic cross-sectional view of a three-dimensional display 50 in which a diffusion plate 35 is provided between the aperture array 30 and the two-dimensional display as a modification of the fourth embodiment of the present invention. The structure shown in FIG. 23 is that when the diffuseness of the light emitted from the color pixels of the two-dimensional display 1 is low and sufficient light intensity distribution cannot be obtained in the openings of the opening array 30, it can A diffuser plate is arranged between the color pixels of the display and the array of openings to adjust the diffuseness of the light.

Example

Hereinafter, examples of the present invention are given to describe the present invention in more detail, but these are merely examples, and the present invention is not limited to the following specific examples. Those skilled in the art can make various changes to the embodiments shown below to implement the present invention, and the changes concerned are included in the scope of the claims of the present application.

A liquid crystal display panel (T221 manufactured by IBM) with a resolution of 3,840×2,400 was used as a two-dimensional display. The color pixels have a stripe structure in which RGB pixels are arranged in the horizontal direction, and the number of pixels of the color pixels is 11,520×2,400 pixels. The pitch of the color pixels is p _x = 0.0415 mm, _py = 0.1245 mm.

Fig. 20 is a schematic diagram showing a pixel structure of a liquid crystal display panel used in an embodiment of the present invention. It shows 6 color pixels in the horizontal direction and 3 in the vertical direction. A color pixel has a multi-region structure divided into upper, lower, left, and right.

As shown in FIG. 20, since the color pixels are not rectangular, the number of vertical pixels N=6 is used to determine the three-dimensional pixels using the above formula (I). In FIG. 20, it can be seen that the horizontal width w is about half of the horizontal pitch _px .

FIG. 21A shows a part of the intensity distribution in the horizontal display direction for a color pixel in an embodiment of the present invention, and FIG. 21B shows a part of the intensity distribution in the horizontal display direction for a three-dimensional pixel in an embodiment of the present invention. Although there are some slight unevenness caused by the pixel structure, a substantially constant intensity distribution can be obtained.

FIG. 22 shows the specifications of a three-dimensional display designed when N=6 according to the present invention. In FIG. 22, type I is a design emphasizing the number of horizontal display directions, and type II is a design emphasizing the number of three-dimensional pixels.

Then, a three-dimensional display was trial-manufactured based on the Type I specification of the present invention. A three-dimensional pixel is formed by using M=12, that is, 36 in the horizontal direction and 6 in the vertical direction, a total of 216 color pixels. The horizontal display direction is 72 directions. Fig. 23 shows a picture of a three-dimensional image acquired by a three-dimensional display. The pictures shown in FIG. 23 represent pictures taken from a plurality of different horizontal directions. As shown in FIG. 23, in the three-dimensional image of the present invention, motion parallax can be observed, and intensity unevenness of the image can hardly be observed.

industrial availability

According to the present invention, there is provided a three-dimensional display capable of displaying a plurality of different images in a horizontal display direction and capable of eliminating color unevenness and intensity unevenness.

Claims (36)

1. A three-dimensional display comprising: A two-dimensional display having a plurality of color pixels arranged in rows extending in the horizontal direction and in columns extending in the vertical direction substantially perpendicular to the horizontal direction, and red and green pixels are periodically arranged on the rows , blue color pixels, the color pixels in the above-mentioned columns are formed in the same color; and A microlens sheet is arranged on the above-mentioned two-dimensional display, and has a plurality of cylindrical lenses extending parallel to each other, and the above-mentioned colored pixels are observed through the cylindrical lenses, The central axis of the above-mentioned cylindrical lens is inclined by an angle θ with respect to the columns of the above-mentioned two-dimensional display, the three-dimensional display, When the horizontal pitch of the above-mentioned colored pixels is p _x , and the vertical pitch of the colored pixels is p _y , a color pixel group of three-dimensional pixels is formed, and the horizontal row of the above-mentioned cylindrical lens is 3M 1. When the column of the above-mentioned one cylindrical lens is composed of N, that is, 3M×N, the above-mentioned color pixels, there is a relational expression of θ=tan ^-1 (3p _x /Np _y ). 2. The three-dimensional display according to claim 1, wherein said two-dimensional display comprises color pixels of a liquid crystal display, an organic EL display, or a plasma display. 3. The three-dimensional display according to claim 1 or 2, wherein said N is a multiple of 3. 4. The three-dimensional display according to any one of claims 1-3, wherein in the structure of the three-dimensional pixel, Np _y ≤ 3Mp _x . 5. The three-dimensional display according to any one of claims 1 to 4, when the horizontal width and the vertical width of the color pixel are respectively w and h, w=3p _x /N. 6. The three-dimensional display according to any one of claims 1 to 5, wherein the value of above-mentioned w is [1-(1/2)(h/ _py )](3p _x /N)～[1+( h/p _y )](3p _x /N). 7. The three-dimensional display according to any one of claims 1 to 6, wherein the value of the h is the same as or similar to the value of the p _y . 8. The three-dimensional display according to any one of claims 1 to 4, when the distribution of the maximum light intensity emitted from the above-mentioned color pixels is a function f(s, t), parallel to the central axis of the above-mentioned cylindrical lens , and the straight line whose horizontal distance is x from the above-mentioned central axis, when expressed by s=-t tanθ+x, the sum of the light intensity in a color pixel on the above-mentioned straight line is given by $\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$ express, The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; ip</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span>$ φ＝tan ^-1 (x/f) Given, where f is the focal length of the cylindrical lens, Each parameter is set so that the above-mentioned formula (I) becomes a substantially constant value regardless of x. 9. A three-dimensional display comprising: A two-dimensional display having a plurality of color pixels arranged in rows extending in the horizontal direction and in columns extending in the vertical direction substantially perpendicular to the horizontal direction, and red and green pixels are periodically arranged in the columns , blue colored pixels; and A microlens sheet is arranged on the above-mentioned two-dimensional display, and has a plurality of cylindrical lenses extending parallel to each other, and the above-mentioned colored pixels are observed through the cylindrical lenses, The central axis of the above-mentioned cylindrical lens is inclined by an angle θ with respect to the columns of the above-mentioned two-dimensional display, the three-dimensional display, When the horizontal pitch of the above-mentioned colored pixels is p _x , and the vertical pitch of the colored pixels is p _y , a color pixel group of three-dimensional pixels is formed, and the horizontal row of the above-mentioned cylindrical lens is 3M 1. When the column of the above-mentioned one cylindrical lens is composed of N, that is, 3M×N, the above-mentioned color pixels, there is a relational expression of θ=tan ^-1 [(1-3/N)p _x / _py ]. 10. The three-dimensional display according to claim 9, wherein said two-dimensional display comprises color pixels of a liquid crystal display, an organic EL display or a plasma display. 11. The three-dimensional display according to claim 9 or 10, wherein said N is a multiple of 3. 12. The three-dimensional display according to any one of claims 9-11, wherein in the structure of the above-mentioned three-dimensional pixel, Np _y ≤ 3Mp _x . 13. The three-dimensional display according to any one of claims 9-12, when the horizontal width and the vertical width of the color pixel are respectively w and h, w=3p _x /N. 14. The three-dimensional display according to any one of claims 9 to 13, wherein the value of above-mentioned w is {1-(1/2)(N/3-1)(h/ _py )}(3p _x / The range of N)≤w≤{1+(N/3-1)(h/p _y )}(3p _x /N). 15. The three-dimensional display according to any one of claims 9 to 14, wherein the value of h is 3p _y /(N-3). 16. The three-dimensional display according to any one of claims 9 to 12, assuming that the distribution of the maximum light intensity emitted from the above-mentioned color pixels is a function f(s, t), parallel to the central axis of the above-mentioned cylindrical lens, When the straight line whose horizontal distance from the above-mentioned central axis is x is represented by s=-t tanθ+x, the sum of the light intensity in one pixel on the above-mentioned straight line is given by $\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$ express, The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; II</span>}<span\; class="notranslate">\; )</span>$ φ＝tan ^-1 (x/f) Given, where f is the focal length of the cylindrical lens, Each parameter is set so that the above-mentioned formula (II) becomes a substantially constant value regardless of x. 17. A three-dimensional display comprising: A two-dimensional display having a plurality of color pixels arranged in rows extending in the horizontal direction and in columns extending in the vertical direction substantially perpendicular to the horizontal direction, and red and green pixels are periodically arranged on the rows , blue color pixels, the color pixels in the above-mentioned columns are formed in the same color; a lenticular sheet, disposed on the above-mentioned two-dimensional display, and having a plurality of cylindrical lenses extending parallel to each other, through which the colored pixels are observed; and An array of openings, disposed between the above-mentioned two-dimensional display and the above-mentioned microlens sheet, having a plurality of openings; The central axis of the above-mentioned cylindrical lens is inclined by an angle θ with respect to the columns of the above-mentioned two-dimensional display, the three-dimensional display, When the horizontal pitch of the above-mentioned color pixels is p _x , the vertical pitch of the above-mentioned color pixels is p _y , the horizontal pitch of the above-mentioned openings is p _x ', and the vertical pitch of the above-mentioned openings is p _y ', a color pixel group constituting a three-dimensional pixel, when the horizontal row of the above-mentioned one cylindrical lens is 3M, and the column of the above-mentioned one cylindrical lens is N, that is, 3M×N color pixels , p _x = p _x ', p _y = p _y ', There is a relational expression of θ=tan ^-1 (3p _x '/Np _y '). 18. The three-dimensional display according to claim 17, wherein said two-dimensional display comprises color pixels of a liquid crystal display, an organic EL display, or a plasma display. 19. The three-dimensional display according to claim 17 or 18, wherein said N is a multiple of 3. 20. The three-dimensional display according to any one of claims 17-19, wherein in the structure of the above-mentioned three-dimensional pixel, Np _y '≤3Mp _x '. 21. The three-dimensional display according to any one of claims 17 to 19, wherein w'=3p _x '/N when the horizontal width and the vertical width of the opening are respectively w' and h'. 22. The three-dimensional display according to any one of claims 17-21, wherein the value of above-mentioned w' is [1-(1/2)(h'/ _py ')](3p _x '/N)～ The range of [1+(h'/p _y ')](3p _x '/N). 23. The three-dimensional display according to any one of claims 17 to 22, wherein the value of h' is the same as or similar to p _y '. 24. The three-dimensional display according to any one of claims 17 to 20, assuming that the distribution of the maximum light intensity emitted from the above-mentioned opening is a function f(s, t), parallel to the central axis of the above-mentioned cylindrical lens, and The horizontal distance of the above-mentioned central axis is a straight line of x, when expressed by s=-t tanθ+x, the sum of the light intensity in a color pixel on the above-mentioned straight line is given by $\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$ express, The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; ip</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; III</span>}<span\; class="notranslate">\; )</span>$ φ＝tan ^-1 (x/f) Given, where f is the focal length of the cylindrical lens, Each parameter is set so that the above-mentioned formula (III) becomes a substantially constant value regardless of x. 25. The three-dimensional display according to any one of claims 17 to 24, wherein said color pixel has multiple regions divided into upper, lower, left, and right. 26. The three-dimensional display according to any one of claims 17-25, further comprising a diffusion plate arranged between the two-dimensional display and the array of openings. 27. A three-dimensional display comprising: A two-dimensional display having a plurality of color pixels arranged in rows extending in the horizontal direction and in columns extending in the vertical direction substantially perpendicular to the horizontal direction, and red and green pixels are periodically arranged in the columns , blue color pixel; a microlens sheet, disposed on the above-mentioned two-dimensional display, and having a plurality of cylindrical lenses extending parallel to each other, through which the colored pixels are observed; and An array of openings, disposed between the above-mentioned two-dimensional display and the above-mentioned microlens sheet, having a plurality of openings; The central axis of the above-mentioned cylindrical lens is inclined by an angle θ with respect to the columns of the above-mentioned two-dimensional display, the three-dimensional display, When the horizontal pitch of the above-mentioned color pixels is p _x , the vertical pitch of the above-mentioned color pixels is p _y , the horizontal pitch of the above-mentioned openings is p _x ', and the vertical pitch of the above-mentioned openings is p _y ', a color pixel group constituting a three-dimensional pixel, when the horizontal row of the above-mentioned one cylindrical lens is 3M, and the column of the above-mentioned one cylindrical lens is N, that is, 3M×N color pixels , p _x = p _x ', p _y = p _y ', There is a relational expression of θ=tan ^-1 [(1-3/N)p _x '/p _y ']. 28. The three-dimensional display according to claim 27, wherein said two-dimensional display comprises color pixels of a liquid crystal display, an organic EL display, or a plasma display. 29. The three-dimensional display according to claim 27 or 28, wherein said N is a multiple of 3. 30. The three-dimensional display according to any one of claims 27-29, wherein in the structure of the above-mentioned three-dimensional pixel, Np _y '≤3Mp _x '. 31. The three-dimensional display according to any one of claims 27 to 30, wherein when the horizontal width and the vertical width of the opening are respectively w' and h', w'=3p _x '/N. 32. The three-dimensional display according to any one of claims 27 to 31, wherein the value of w' is {1-(1/2)(N/3-1)(h/ _py ')}(3p The range of _x '/N)≤w'≤{1+(N/3-1)(h/p _y ')}(3p _x '/N). 33. The three-dimensional display according to any one of claims 27 to 32, wherein the value of h' is 3p _y '/(N-3). 34. The three-dimensional display according to any one of claims 27 to 30, assuming that the distribution of the maximum light intensity emitted from the above-mentioned opening is a function f(s, t), parallel to the central axis of the above-mentioned cylindrical lens, and The horizontal distance of the above-mentioned central axis is a straight line of x, when expressed by s=-t tanθ+x, the sum of the light intensity in a color pixel on the above-mentioned straight line is given by $\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}{\overset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dt</span>}$ express, The light intensity of the overall horizontal display direction  of the above-mentioned three-dimensional pixels is given by ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; IV</span>}<span\; class="notranslate">\; )</span>$ φ＝tan ^-1 (x/f) Given, where f is the focal length of the cylindrical lens, Each parameter is set so that the above-mentioned formula (IV) becomes a substantially constant value regardless of x. 35. The three-dimensional display according to any one of claims 27 to 34, wherein the color pixel has multiple regions divided into up, down, left, and right. 36. The three-dimensional display according to any one of claims 27-35, further comprising a diffusion plate arranged between the two-dimensional display and the array of openings.

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