Parallax barrier for autostereoscopic display, autostereoscopic display, and method for designing parallax barrier for autostereoscopic display

• US 8,964,009 B2
• Filed: 07/12/2010
• Issued: 02/24/2015
• Est. Priority Date: 07/13/2009
• Status: Expired due to Fees

• Current Assignee: Kenji Yoshida
• Original Assignee: Kenji Yoshida
• Inventors: Yoshida, Kenji
• Primary Examiner(s): Perungavoor, Sath V
• Assistant Examiner(s): AYNALEM, NATHNAEL B
• Application Number:
  US13/384,071
• Publication Number:
  US 20120182407A1
• Time in Patent Office: 1,688 Days
• Field of Search: 345/55, 345/419, 348/53, 348/54, 348/55, 348/58, 348/59, 348/60, 359/462, 359/463, 359/620
• US Class Current: 348/54
• CPC Class Codes: G02B 27/60 Systems using moiré fringes
• CPC Class Codes: G02B 30/27 involving lenticular arrays
• CPC Class Codes: G02B 30/30 involving parallax barriers
• CPC Class Codes: G03B 35/18 by simultaneous viewing
• CPC Class Codes: H04N 13/31 using parallax barriers
• CPC Class Codes: H04N 13/317 using slanted parallax optics
• CPC Class Codes: H04N 13/373 for tracking forward-backward translational head movements, i.e. longitudinal movements

Abstract

Moiré generated in an autostereoscopic display utilizing a parallax barrier method is cancelled. The interval between visible light transmitting sections that are abutting in the horizontal direction of a parallax barrier is determined using: the average number of subpixels constituting one pixel for three-dimensional display in one row in the horizontal direction; the width of a subpixel, which forms a display; the distance from a predetermined diagonal moiré canceling position to the parallax barrier; the number of viewpoints of a video image used for displaying an autostereoscopic video image; and the distance (Z) from the image display surface of the display to the parallax barrier.

Claims

1. A parallax barrier for an autostereoscopic display wherein

the parallax barrier for an autostereoscopic display is provided with a distance Z from an image display surface of a display on which a plurality of pixels each having horizontally arranged three subpixels displaying R, G, and B are arranged in horizontal and vertical directions,

values relating to sizes and arrangements of a plurality of visible light transmitting sections and a value of the distance Z are calculated and designed based on a predetermined designing condition, and

in autostereoscopic viewing under a condition in which:

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph;

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph;

a distance between pupils of left and right eyes of a subject person of video image presentation is defined as W; and

a number of viewpoints of the video images for creating the autostereoscopic video image is defined as N, and

in a design condition in which;

a most appropriate three-dimensionally viewable position is preset and a distance from such a position to the parallax barrier is defined as L1; and

a diagonal moire cancelling position is preset and a distance from such a position to the parallax barrier is defined as L2,

the parallax barrier is designed by

determining a value of the distance Z from the image display surface of the display to the parallax barrier by a following function (1); and

determining a value of an interval Hh between a plurality of horizontally abutting visible light transmitting sections constituting the parallax barrier by a following function (2);

4. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein, in autostereoscopic viewing under a condition in which:

a shape of an edge of slits as the visible light transmitting sections constituting the parallax barrier is a staircase pattern, or a skewered dumpling like shape in which any of circular arcs, elliptic arcs,

and polygons are repeatedly concatenated, or a shape of the visible light transmitting sections constituting the parallax barrier is a plurality of independently formed holes;

a number of one unit of the visible light transmitting sections of the repeated shapes or the visible light transmitting sections of the plurality of holes in a vertical direction corresponding to one subpixel is defined as β

; and

a height of subpixels forming the display is defined as Pv, and

in a design condition in which;

the distance Z is calculated by the formula (I); and

a horizontal moire cancelling position is preset and a distance from such a position to the parallax barrier is defined as L3,

the parallax barrier is designed by;

determining a value of an interval Hv between vertically abutting visible light transmitting sections of the staircase patterned or the skewered dumpling like shaped, or the plurality of holes by a following formula (6);

5. The parallax barrier for an autostereoscopic display according to claim 4, wherein generation of horizontal moire is prevented by irregularly arranging only vertical arrangement positions (arrangement starting positions) of the plurality of visible light transmitting sections of the staircase pattern, the skewered dumpling like shape, or the plurality of holes for each of the slits that abut in a horizontal direction.

6. The parallax barrier for an autostereoscopic display according to claim 5, wherein the irregularity is characterized by determining the arrangement positions (arrangement starting positions) using random digits.

7. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein, in autostereoscopic viewing under a condition in which:

a shape of an edge of slits as the visible light transmitting sections constituting the parallax barrier is a staircase pattern, or a skewered dumpling like shape in which any of circular arcs, elliptic arcs,

and polygons are repeatedly concatenated, or a shape of the visible light transmitting sections constituting the parallax barrier is a plurality of independently formed holes;

a number of one unit of the visible light transmitting sections of the repeated shapes or the visible light transmitting sections of the plurality of holes in a vertical direction corresponding to one subpixel is defined as β

;

a vertical resolution of the display is defined as Jr; and

a height of subpixels forming the display is defined as Pv, and

in a design condition in which;

the distance Z is calculated by the formula (I); and

a position closest to the parallax barrier among positions from which one line of horizontal moire is seen is preset, and a distance from such a position to the parallax barrier is defined as L3n,

the parallax barrier is designed by;

determining a value of a number Mv of one unit of the visible light transmitting sections of the repeated shape or visible light transmitting sections of the plurality of holes in a vertical direction from a visible light transmitting section of the shape corresponding to a subpixel at an upper end of the display to a visible light transmitting section of the shape corresponding to a subpixel at a lower end of the display seen from a horizontal moire cancelling position by a following formula (7); and

determining a value of an interval Hv of vertically abutting visible light transmitting sections of the staircase patterned, the skewered dumpling like shaped, or the plurality of holes by a following formula (8);

8. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein, in autostereoscopic viewing under a condition in which:

a shape of an edge of slits as the visible light transmitting sections constituting the parallax barrier is a staircase pattern, or a skewered dumpling like shape in which any of circular arcs, elliptic arcs,

and polygons are repeatedly concatenated, or a shape of the visible light transmitting sections constituting the parallax barrier is a plurality of independently formed holes;

a number of one unit of the visible light transmitting sections of the repeated shape or the visible light transmitting sections of the plurality of holes in a vertical direction corresponding to one subpixel is defined as β

;

a vertical resolution of the display is defined as Jr; and

a height of subpixels forming the display is defined as Pv, and

in a design condition in which;

the distance Z is calculated by the formula (I); and

a position farthest to the parallax barrier among positions from which one line of diagonal moire is seen is preset, and a distance from such a position to the parallax barrier is defined as L3f,

the parallax barrier is designed by;

determining a value of a number Mv of one unit of the visible light transmitting sections of the repeated shape or visible light transmitting sections of the plurality of holes in a vertical direction from a visible light transmitting section of the shape corresponding to a subpixel at an upper end of the display to a visible light transmitting section of the shape corresponding to a subpixel at a lower end of the display seen from a horizontal moire cancelling position by a following formula (7); and

determining a value of an interval Hv of vertically abutting visible light transmitting sections of the staircase patterned, the skewered dumpling like shaped, or the plurality of holes by a following formula (9);

9. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein

in autostereoscopic viewing under a condition in which:

a distance between pupils of left and right eyes of a subject person of video image presentation is defined as W;

a width of an effective viewable area seen by one eye of the subject person of video image presentation through visible light transmitting sections of width Sh constituting the parallax barrier from the most appropriate three-dimensionally viewable position is defined as Vh;

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph; and

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph,

the parallax barrier is designed by;

determining a value of the width Sh of the visible light transmitting sections constituting the parallax barrier by a following formula (10);

10. A designing method of the parallax barrier for an autostereoscopic display according to claim 4, wherein, in autostereoscopic viewing under a condition in which:

a shape of an edge of slits as the visible light transmitting sections constituting the parallax barrier is a staircase pattern, or a skewered dumpling like shape in which any of circular arcs, elliptic arcs,

and polygons are repeatedly concatenated, or the shape of the visible light transmitting sections constituting the parallax barrier is independently formed plurality of holes;

a height of a predetermined effective viewable area seen from a subject person of video image presentation through visible light transmitting sections of height Sv constituting the parallax barrier from the most appropriate three-dimensionally viewable position is defined as Vv;

an interval of the visible light transmitting sections of the plurality of holes that abut one another in a vertical direction of the parallax barrier is defined as Hv; and

an aperture ratio (a coefficient for Hv) of the vertical direction is defined as λ

, and in a design condition in which;

a most appropriate three-dimensionally viewable position is preset, and a distance from such a position to the parallax barrier is defined as L1; and

the distance Z is calculated by the formula (I),

a value of the height Sv of visible light transmitting sections of the staircase patterned, the skewered dumpling like shaped, or the plurality of holes is determined by a following formula (11) or (11)′

;

11. The designing method of the parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein:

using the distance Z calculated by the formula (I);

a distance W between pupils of left and right eyes of a subject person of video image presentation; and

a width Vh of an effective viewable area seen by one eye of the subject person of video image presentation through visible light transmitting sections of width Sh constituting the parallax barrier from the most appropriate three-dimensionally viewable position,

the parallax barrier is designed by;

determining a closest distance L1n within an appropriate three-dimensionally viewable area by a following formula (12);

determining a farthest distance L1f within the appropriate three-dimensionally viewable area by a following formula (13); and

presetting a distance L2 from the diagonal moire cancelling position to the parallax barrier within the appropriate three-dimensionally viewable area from L1n to L1f;

12. The designing method of the parallax barrier for an autostereoscopic display according to any one of claims 1 to 3 wherein:

a distance L1 from the most appropriate three-dimensionally viewable position to the parallax barrier is set as a same distance as a distance L2 from the diagonal moire cancelling position to the parallax barrier.

13. The parallax barrier for an autostereoscopic display according to claim 4, wherein:

a shape of an edge of slits as the visible light transmitting sections constituting the parallax barrier is a staircase pattern, or a skewered dumpling like shape in which any of circular arcs, elliptic arcs,

and polygons are repeatedly concatenated, or a shape of the visible light transmitting sections constituting the parallax barrier is independently formed plurality of holes;

values relating to sizes and arrangements of the plurality of visible light transmitting sections and a value of the distance Z are calculated and designed based on a predetermined design condition; and

a distance L1 from the most appropriate three-dimensionally viewable position to the parallax barrier is preset as a same distance as a distance L2 from the diagonal moire cancelling position to the parallax barrier and a distance L3 from the horizontal moire cancelling position to the parallax barrier.

14. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3 wherein, in autostereoscopic viewing under a condition in which:

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph; and

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph,

the parallax barrier is designed by;

defining a maximum area on an image display surface intended to be seen by one eye of a subject person of video image presentation through visible light transmitting sections of width Sh constituting the parallax barrier from the most appropriate three-dimensionally viewable position as a rectangular area;

determining a width Vh max of the rectangular area as being 2×

α

Ph or more and less than 3×

α

Ph;

determining a width Vh of a predetermined effective viewable area seen by one eye of the subject person of video image presentation through visible light transmitting sections of width Sh constituting the parallax barrier as being α

Ph or more and Vh max or less.

15. The designing method of the parallax barrier for an autostereoscopic display according to claim 4 wherein, in autostereoscopic viewing under a condition in which:

an interval of vertically abutting subpixels is defined as Hpv; and

a number of one unit of the visible light transmitting sections of the repeated shape or the visible light transmitting sections of the plurality of holes in a vertical direction corresponding to one subpixel is defined as β

,

the parallax barrier is designed by

determining an interval Hv of vertically abutting visible light transmitting sections of the staircase patterned, the skewered dumpling like shaped, or the plurality of holes using an equation Hv=Hpv/β

(β

is a natural number).

16. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein

a calibration line of vertical slit shape that transmits visible light is provided at least either left end or right end thereof, and

the parallax barrier is fixed to the display by calibration operation by:

being placed on the display;

adjusting a position so that visible light seen through the calibration line becomes a same color; and

being moved in a parallel manner to a position at which a subject person of video image presentation does not see the calibration line.

17. The parallax barrier for an autostereoscopic display according to claim 16, wherein a width of the calibration line Ch is determined by a following formula (14) using a width Ph of subpixels forming the display, and a distance L4 from one eye of an operator to the parallax barrier when performing the calibration operation:

18. The designing method of a parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein

the distance Z from an image display surface of the display to the parallax barrier is determined by, instead of the formula (I), the following formula (15) using:

a width Vh of an effective viewable area seen by one eye through visible light transmitting sections of width Sh from a closest distance L1n from the parallax barrier to a predetermined appropriate three-dimensionally viewable area; and

a distance W between pupils of left and right eyes of a subject person of video image presentation;

19. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3, wherein

the distance Z from an image display surface forming the display to the parallax barrier is determined by, instead of the formula (I), the following formula (16) using:

a width Vh of an effective viewable area seen by one eye through visible light transmitting sections of width Sh from a farthest distance L1f from the parallax barrier to a predetermined appropriate three-dimensionally viewable area; and

a distance W between pupils of left and right eyes of a subject person of video image presentation;

20. The parallax barrier for an autostereoscopic display according to any one of claims 4 to 19, wherein, in a case in which:

the display is a plasma display;

a shape of visible light transmitting sections constituting the parallax barrier is a plurality of independently formed holes;

a width of the visible light transmitting sections constituting the parallax barrier is defined as Sh;

a height of the visible light transmitting sections of the plurality of holes is defined as Sv; and

an effective maximum amplitude that blocks electromagnetic waves generated from the plasma display is defined as Er, the parallax barrier is designed by;

determining a value of a number β

of the visible light transmitting sections in a vertical direction corresponding to the one subpixel by a following formula (17) (calculating a smallest integer equal to or more than a value calculated by calculation between □

s the same goes for a formula (18);

determining a value of a number γ

of the visible light transmitting sections in a horizontal direction corresponding to the one subpixel by the following formula (18); and

forming with material that blocks electromagnetic waves generated from the plasma display;

21. The parallax barrier for an autostereoscopic display according to claim 4, wherein the visible light transmitting sections of the plurality of independently formed holes constituting the parallax barrier are an elliptic arc shape, a Japanese lantern shape with flattened top and button elliptic arcs, or a convex polygon with more than of four even number corners.

22. The parallax barrier for an autostereoscopic display according to claim 21, wherein the visible light transmitting sections of the plurality of independently formed holes constituting the parallax barrier are of a shape formed by inclining in a horizontal direction, by a predetermined angle, the elliptic arc shape, the Japanese lantern shape with flattened top and button elliptic arcs, or the convex polygon with more than four even number corners.

23. The parallax barrier for an autostereoscopic display according to claim 4 wherein

the visible light transmitting sections of a plurality of independently formed holes constituting the parallax barrier is designed by:

determining a rectangular area which is a maximum area on an image display surface intended to be seen by one eye of a subject person of video image presentation through visible light transmitting sections of width Sh constituting the parallax barrier from the most appropriate three-dimensionally viewable position;

defining a shape inscribed in upper, lower, left, and right sides or only left and right sides of an area which is a like figure with the rectangular area and is formed by, using either left or right eyes of the subject person of video image presentation at the most appropriate three-dimensionally viewable position as a base point, intersections of line segments connecting the either eye to the rectangular area and the parallax barrier surface; and

defining an area on a pixel array surface seen by the subject person of video image presentation through the hole using either left or right eyes of the subject person of video image presentation at the most appropriate three-dimensionally viewable position as a base point, as an effective viewable area of a like figure with the hole.

24. The parallax barrier for an autostereoscopic display according to any one of claims 1 to 3 wherein

the parallax barrier is a plate type transparent medium, and reflection is prevented by:

providing visible light impermeable sections on a side of a subject person of video image presentation; and

forming the visible light impermeable sections with material that absorbs visible light and/or material that diffusely reflects visible light.

25. An autostereoscopic display using the parallax barrier for an autostereoscopic display according to any one of claims 1 to 3.

2. A parallax barrier for an autostereoscopic display wherein

the parallax barrier for an autostereoscopic display is provided with a distance Z from an image display surface of a display on which a plurality of pixels each having horizontally arranged three subpixels displaying R, G, and B are arranged in horizontal and vertical directions,

values relating to sizes and arrangements of a plurality of visible light transmitting sections and a value of the distance Z are calculated and designed based on a predetermined designing condition, and

in autostereoscopic viewing under a condition in which:

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph;

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph;

a distance between pupils of left and right eyes of a subject person of video image presentation is defined as W;

a horizontal resolution of the display is defined as Ir; and

a number of viewpoints of the video images for creating the autostereoscopic video image is defined as N, and

in a design condition in which;

a most appropriate three-dimensionally viewable position is preset and a distance from such a position to the parallax barrier is defined as L1; and

an appropriate three-dimensionally viewable position is preset as a position closest to the parallax barrier among positions from which one line of diagonal moire is seen, and a distance from such an appropriate three-dimensionally viewable position to the parallax barrier is defined as L2n,

the parallax barrier is designed by;

determining a value of the distance Z from the image display surface of the display to the parallax barrier by a following function (1);

determining a value of a number Mh of visible light transmitting sections in a horizontal direction from a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a left end of the display to a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a right end of the display seen from a diagonal moire cancelling position by a following formula (3); and

,

determining a value of an interval Hh between a plurality of horizontally abutting visible light transmitting sections constituting the parallax barrier by a following function (4);

3. A parallax barrier for an autostereoscopic display wherein:

the parallax barrier for an autostereoscopic display is provided with a distance Z from an image display surface of a display on which a plurality of pixels each having horizontally arranged three subpixels displaying R, G, and B are arranged in horizontal and vertical directions;

values relating to sizes and arrangements of a plurality of visible light transmitting sections and a value of the distance Z are calculated and designed based on a predetermined designing condition; and

in autostereoscopic viewing under a condition in which;

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph;

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph;

a distance between pupils of left and right eyes of a subject person of video image presentation is defined as W;

a horizontal resolution of the display is defined as Ir; and

a number of viewpoints of the video images for creating the autostereoscopic video image is defined as N, and in a design condition in which;

a most appropriate three-dimensionally viewable position is preset and a distance from such a position to the parallax barrier is defined as L1; and

an appropriate three-dimensionally viewable position is preset as a position farthest to the parallax barrier among positions from which one line of diagonal moire is seen, and a distance from such an appropriate three-dimensionally viewable position to the parallax barrier is defined as L2f, the parallax barrier is designed by;

determining a value of the distance Z from the image display surface of the display to the parallax barrier by a following function (1);

determining a value of a number Mh of visible light transmitting sections in a horizontal direction from a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a left end of the display to a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a right end of the display seen from a diagonal moire cancelling position by a following formula (3); and

determining a value of an interval Hh between a plurality of horizontally abutting visible light transmitting sections constituting the parallax barrier by a following function (5);

26. A designing method of a parallax barrier for an autostereoscopic display that calculates and designs:

values relating to sizes and arrangements of a plurality of visible light transmitting sections constituting the parallax barrier provided with a distance Z from an image display surface of a display on which a plurality of pixels each having horizontally arranged three subpixels displaying R, G, and B are arranged in horizontal and vertical directions, and a value of the distance Z, based on a predetermined designing condition, wherein in autostereoscopic viewing under a condition in which;

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph;

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph;

a distance between pupils of left and right eyes of a subject person of video image presentation is defined as W; and

a number of viewpoints of the video images for creating the autostereoscopic video image is defined as N, and

in a design condition in which;

a most appropriate three-dimensionally viewable position is preset and a distance from such a position to the parallax barrier is defined as L1; and

a diagonal moire cancelling position is preset and a distance from such a position to the parallax barrier is defined as L2,

a value of the distance Z from the image display surface of the display to the parallax barrier is determined by a following function (1); and

a value of an interval Hh of a plurality of horizontally abutting visible light transmitting sections constituting the parallax barrier is determined by a following function (2);

27. A designing method of a parallax barrier for an autostereoscopic display that calculates and designs:

values relating to sizes and arrangements of a plurality of visible light transmitting sections constituting the parallax barrier provided with a distance Z from an image display surface of a display on which a plurality of pixels each having horizontally arranged three subpixels displaying R, G, and B are arranged in horizontal and vertical directions, and

a value of the distance Z, based on a predetermined designing condition, wherein in autostereoscopic viewing under a condition in which;

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph;

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph;

a distance between pupils of left and right eyes of a subject person of video image presentation is defined as W;

a horizontal resolution of the display is defined as Ir; and

a number of viewpoints of the video images for creating the autostereoscopic video image is defined as N, and

in a design condition in which;

a most appropriate three-dimensionally viewable position is preset and a distance from such a position to the parallax barrier is defined as L1; and

an appropriate three-dimensionally viewable position is preset as a position closest to the parallax barrier among positions from which one line of diagonal moire is seen, and a distance from such an appropriate three-dimensionally viewable position to the parallax barrier is defined as L2n,

a value of the distance Z from the image display surface of the display to the parallax barrier is determined by a following function (1);

a value of a number Mh of visible light transmitting sections in a horizontal direction from a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a left end of the display to a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a right end of the display seen from a diagonal moire cancelling position is determined by a following formula (3); and

,

a value of an interval Hh of a plurality of horizontally abutting visible light transmitting sections constituting the parallax barrier is determined by a following function (4);

28. A designing method of a parallax barrier for an autostereoscopic display that calculates and designs:

values relating to sizes and arrangements of a plurality of visible light transmitting sections constituting the parallax barrier provided with a distance Z from an image display surface of a display on which a plurality of pixels each having horizontally arranged three subpixels displaying R, G, and B are arranged in horizontal and vertical directions, and

a value of the distance Z, based on a predetermined designing condition, wherein in autostereoscopic viewing under a condition in which;

an average number of subpixels in a horizontal direction constituting pixels for three-dimensional display for one viewpoint of an autostereoscopic video image created from video images of a plurality of viewpoints is defined as α

;

a width of subpixels constituting the display is defined as Ph;

a distance between centers of pixels for three-dimensional display that display video images of neighboring viewpoints is defined as α

Ph;

a distance between pupils of left and right eyes of a subject person of video image presentation is defined as W;

a horizontal resolution of the display is defined as Ir; and

a number of viewpoints of the video images for creating the autostereoscopic video image is defined as N, and

in a design condition in which;

a most appropriate three-dimensionally viewable position is preset and a distance from such a position to the parallax barrier is defined as L1; and

an appropriate three-dimensionally viewable position is preset as a position farthest from the parallax barrier among positions from which one line of diagonal moire is seen, and a distance from such an appropriate three-dimensionally viewable position to the parallax barrier is defined as L2f,

a value of the distance Z from the image display surface of the display to the parallax barrier is determined by a following function (1);

a value of a number Mh of visible light transmitting sections in a horizontal direction from a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a left end of the display to a visible light transmitting section of the parallax barrier corresponding to pixel units for three-dimensional display at a right end of the display seen from a diagonal moire cancelling position is determined by a following formula (3); and

,

a value of an interval Hh of a plurality of horizontally abutting visible light transmitting sections constituting the parallax barrier is determined by a following function (5);