JP5850312B2 - Optical sheet and image display device - Google Patents

Description

  The present invention relates to an optical sheet that includes a plurality of unit lenses arranged in a predetermined arrangement pattern, and in particular, effectively suppresses the occurrence of moiré and density unevenness due to the arrangement pattern of the plurality of unit lenses. It is related with the optical sheet which can do. The present invention also relates to an image display apparatus having this optical sheet.

  Conventionally, optical sheets having unit lenses have been used in various fields. As an example, Patent Document 1 discloses a microlens array sheet disposed on an image forming surface of an image forming apparatus that forms an image. An optical sheet that is used by being superimposed on an image forming apparatus is provided mainly for the purpose of adjusting luminance characteristics, particularly viewing angle characteristics. In an optical sheet having a microlens formed by two-dimensionally arranging unit lenses, the optical characteristics, particularly the viewing angle characteristics, in each direction can be adjusted by the cross-sectional shape of the unit lenses and the planar arrangement of the unit lenses.

JP-A-10-39109

  By the way, an image forming apparatus represented by a plasma display panel (hereinafter also simply referred to as “PDP”), a liquid crystal display panel (hereinafter also simply referred to as “LCD panel”), and the like has a pixel array having a repeating cycle. A desired image is formed by controlling light for each pixel. For this reason, as described in paragraph 0081 of Patent Document 1, a striped pattern resulting from interference between the periodicity of the pixel array and the periodicity of the unit lens, that is, moire (interference fringes) is visually recognized. The quality of the displayed image may be deteriorated.

  From the viewpoint of suppressing the occurrence of moire, making the arrangement of unit lenses irregular has also been studied. However, when the unit lenses are irregularly arranged, another problem may occur, such as unevenness in density according to the density of the unit lenses.

  The present invention has been made in view of the above points, and an object thereof is to provide an optical sheet that can make both density unevenness and moire inconspicuous, and an image display device including the optical sheet. .

The first optical sheet according to the present invention is:
An optical sheet used in an overlapping manner with an image forming apparatus,
A sheet-like body,
A plurality of unit lenses arranged on one surface of the main body,
On one surface of the main body, a line portion composed of a boundary line segment extending between two adjacent unit lenses is defined,
Both ends of each boundary line segment of the line part form a branch point connecting to two or more other boundary line segments,
The line portion defines a closed region surrounded by the boundary line segment, and the unit lenses are arranged on the main body portion so that one unit lens is disposed in one closed region. ,
The line portion includes a closed region surrounded by five boundary segments, a closed region surrounded by six boundary segments, and a closed region surrounded by seven boundary segments. Including an area containing at least two types selected from
The shape or area of the plurality of closed regions surrounded by the same number of boundary lines out of 5, 6, or 7 included in the region is not constant.

The second optical sheet according to the present invention is:
An optical sheet used in an overlapping manner with an image forming apparatus,
A sheet-like body,
A plurality of unit lenses arranged on one surface of the main body,
On one surface of the main body, a line portion composed of a boundary line segment extending between two adjacent unit lenses is defined,
Both ends of each boundary line segment of the line part form a branch point connecting to two or more other boundary line segments,
The line portion defines a closed region surrounded by the boundary line segment, and the unit lenses are arranged on the main body portion so that one unit lens is disposed in one closed region. ,
The line portion includes a region where an average number of boundary line segments extending from one branch point is 3.0 or more and less than 4.0,
The shape or area of the plurality of closed regions included in the region is not constant.

  In the region of the line portion of the second optical sheet according to the present invention, the average of the number of boundary line segments connected at one branch point may be larger than 3.0.

  In the region of the line portion of the second optical sheet according to the present invention, the average of the number of boundary line segments connected at one branch point may be 3.0.

In the second optical sheet according to the present invention, the area of the line portion includes a closed area surrounded by five boundary line segments, a closed area surrounded by six boundary line segments, and 7. Includes at least two types selected from the closed area surrounded by the border of the book,
The shape or area of the plurality of closed regions surrounded by the same number of boundary line segments among the five, six, or seven included in the region may not be constant.

  In the first or second optical sheet according to the present invention, the region of the line portion may include a closed region surrounded by six boundary line segments.

  In the first or second optical sheet according to the present invention, the region of the line portion may include the largest number of closed regions surrounded by six boundary line segments.

In the first or second optical sheet according to the present invention, among the closed regions included in the region of the line portion, when the number of closed regions surrounded by k boundary line segments is N _k ,
When k is an integer satisfying 3 ≦ k ≦ 5, N _k ≦ N _{k + 1} is satisfied,
When k is an integer satisfying 6 ≦ k, N _k ≧ N _{k + 1} may be satisfied.

In the region of the line portion of the first or second optical sheet according to the present invention,
The plurality of unit lenses are arranged without a gap on the one surface of the main body,
The boundary line segment may extend along the outer contour of the unit lens on one surface of the main body.

In the region of the line portion of the first or second optical sheet according to the present invention,
All or a part of the plurality of unit lenses are arranged on the one surface of the main body part and spaced apart from each other,
The boundary line segment may extend at a position equidistant from the outer contour of two adjacent unit lenses on one surface of the main body.

In the region of the line portion of the first or second optical sheet according to the present invention,
All or a part of the plurality of unit lenses are arranged on the one surface of the main body part and spaced apart from each other,
In the direction perpendicular to the boundary line segment at the center position from the center position on the boundary line segment, at the outer contour of each unit lens in the two closed regions located on both sides of the boundary line segment The distances along may be the same.

An image display device according to the present invention includes:
An image forming apparatus;
Any of the above-described optical sheets according to the present invention provided on the image forming apparatus.

  According to the present invention, it is possible to make the moire inconspicuous very effectively while suppressing the occurrence of density unevenness.

FIG. 1 is a diagram for explaining an embodiment of the present invention, and is a cross-sectional view showing a schematic configuration of an image display device. FIG. 2 is a partial perspective view showing the optical sheet. FIG. 3 is a cross-sectional view taken along the normal direction of the optical sheet in FIG. 2 and is a diagram for explaining an optical function of the optical sheet. FIG. 4 is a view showing an optical sheet different from the embodiment shown in FIG. 3 in the same cross section as FIG. FIG. 5 is a plan view showing the optical sheet from the normal direction, and is a diagram for explaining an arrangement pattern of unit lenses and a pattern of a line portion included in the optical sheet. FIG. 6 is a partially enlarged view of FIG. 5 for explaining the unit lens arrangement pattern and the line portion pattern. FIG. 7 is a graph showing the number of closed regions surrounded by each number of boundary line segments. FIG. 8 is a plan view for explaining a pixel arrangement of an image forming apparatus that can be incorporated in the image display apparatus of FIG. FIG. 9 is a plan view showing a state in which the optical sheet on which unit lenses are arranged in the arrangement pattern of FIG. 5 and the image forming apparatus having the pixel arrangement shown in FIG. 8 are overlapped. FIG. 10 is a diagram for explaining a method of designing the pattern of the line portion shown in FIG. 5, and is a diagram showing a method of determining a generating point. FIG. 11 is a diagram for explaining a method of designing the pattern of the line portion shown in FIG. 5, and is a diagram showing a method for determining a generating point. FIG. 12 is a diagram for explaining a method of designing the pattern of the line portion shown in FIG. 5, and is a diagram showing a method for determining a generating point. FIGS. 13A to 13D are diagrams showing the determined mother point group in the absolute coordinate system and the relative coordinate system, and are diagrams for explaining the degree of dispersion of the mother point group. FIG. 14 is a diagram for explaining a method of designing the line portion pattern shown in FIG. 5, and shows a method of determining a line portion pattern by creating a Voronoi diagram from the determined mother point. FIG. FIG. 15 is a partial plan view showing a modification of the optical sheet from the normal direction, and is a diagram for explaining a modification of the optical sheet. FIG. 16 is a plan view showing another modification of the optical sheet. FIG. 17 is a plan view for explaining an example of the arrangement pattern of the optical sheet according to the related art. FIG. 18 is a plan view for explaining another example of the arrangement pattern of the optical sheet according to the related art. FIG. 19 is a plan view showing a state in which the optical sheet on which unit lenses are arranged in the arrangement pattern of FIG. 17 and the image forming apparatus having the pixel arrangement shown in FIG. 8 are overlapped. 20 is a plan view showing a state in which the optical sheet in which unit lenses are arranged in the arrangement pattern of FIG. 18 and the image forming apparatus having the pixel arrangement shown in FIG. 8 are overlaid.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the drawings attached to the present specification, for the sake of illustration and ease of understanding, the scale, the vertical / horizontal dimension ratio, and the like are appropriately changed and exaggerated from those of the actual product.

  1 to 15 are diagrams for explaining an embodiment according to the present invention. Among these, FIG. 1 is a cross-sectional view showing the image display device in a cross section along the normal direction to the image forming surface of the image display device. FIG. 2 is a partial perspective view showing an optical sheet incorporated in the image display device, and FIGS. 3 and 4 are cross-sectional views for explaining an optical function of a unit lens of the optical sheet. FIG. 5 and FIG. 6 are diagrams illustrating the optical sheet incorporated in the image display device from the normal direction, and are diagrams for explaining the arrangement pattern of the unit lenses. FIG. 7 is a graph showing the relationship between the number of boundary lines surrounding the closed area and the number of closed areas surrounded by each number of boundary lines for the arrangement pattern shown in FIG. FIG. 8 is a diagram for explaining the pixel arrangement of the image forming apparatus. FIG. 9 is a diagram illustrating the unit lens array pattern of the optical sheet and the pixel array of the image forming apparatus in an overlaid state. 10 to 14 are diagrams for explaining a method of determining the arrangement pattern of the unit lenses shown in FIG.

  As shown in FIG. 1, the image display apparatus 10 includes an image forming apparatus 15 that can form an image, and a light output side (image observer side, hereinafter referred to as an image observer (side)) of the image forming apparatus 15. And an optical sheet 30 which is also abbreviated as “side”). In the illustrated example, the light exit surface of the optical sheet 30 forms the display surface (light exit surface) 10 a of the image display device 10, and the observer views the image formed by the image forming device 15 via the optical sheet 30. Will observe.

  The image forming apparatus 15 is configured as various apparatuses for forming an image, for example, an apparatus including a plasma display panel (PDP), a liquid crystal display panel (LCD), a cathode ray tube (CRT), an organic EL display panel, and the like. obtain. The image forming apparatus 15 has a large number of regularly arranged pixels, and is configured to form an image by controlling image light for each pixel.

  FIG. 8 discloses an example of a pixel array of the image forming apparatus (image display panel) 15. As shown in FIG. 8, one pixel P includes a sub-pixel (sub-pixel) RP that emits red light, a sub-pixel GP that emits green light, and a sub-pixel BP that emits blue light. That is, the image forming apparatus 15 can form an image in color. In the example shown in FIG. 8, the pixels P are formed as a so-called stripe arrangement. That is, the sub-pixel RP that emits red light, the sub-pixel GP that emits green light, and the sub-pixel BP that emits blue light are successively arranged in one direction (vertical direction in FIG. 8). On the other hand, the sub-pixel RP that emits red light, the sub-pixel GP that emits green light, and the sub-pixel BP that emits blue light are sequentially repeated one by one in a direction orthogonal to the one direction (the horizontal direction in FIG. 8). Are lined up. FIG. 8 shows the arrangement of the pixels P in a state where the image forming apparatus 15 is observed from the normal direction to the image forming surface (light exit surface) 15a of the image forming apparatus 15.

  In the example illustrated in FIG. 1, the optical sheet 30 is disposed apart from the image forming surface 15 a of the image forming apparatus 15. However, the optical sheet 30 may be disposed in contact with the image forming surface 15a of the image forming apparatus 15, or may be bonded to the image forming surface 15a of the image forming apparatus 15 through an adhesive or the like. Good. Note that “adhesion” used in this specification includes the meaning of “adhesion”.

  Further, in the illustrated image display device 10, only the optical sheet 30 is disposed on the light output side of the image forming device 15. However, a sheet-like member or layer expected to exhibit various functions may be further provided in the image forming apparatus 10. Moreover, the optical sheet demonstrated here may be laminated | stacked with another sheet-like member (layer), and you may make it handle as a laminated body. Various sheet-like members (layers) may be disposed on the light incident side of the optical sheet 30 or may be disposed on the light exit side of the optical sheet 30. As an example of such a sheet-like member (layer), an electromagnetic wave shielding material that blocks electromagnetic waves in a specific wavelength range, a polarizing plate, and an optical member that has light-transmitting properties and is provided with a light-shielding portion to absorb unnecessary light ( For example, refer to Japanese Patent Application Laid-Open No. 2008-170975), a layer (member) having a filter function that shields radiation in a specific wavelength range emitted from the image forming apparatus 15, and a layer (member) having a desired optical function ), A layer (member) provided with other functions such as a protective function, an antireflection layer, and an antiglare layer.

  Furthermore, when the optical sheet 30 is bonded to another sheet-like member (layer) or an image forming apparatus via an adhesive, the adhesive is provided with a filter function that can absorb light in a specific wavelength range. Also good. Specifically, one or more of various functions such as a function of absorbing near infrared rays, a function of absorbing neon light, and a function of absorbing ultraviolet rays (UV) may be imparted to the adhesive.

  In the present specification, the “light exit side” refers to the downstream side (observer side, in FIG. 1) of the light traveling direction from the image forming apparatus 15 to the observer through the optical sheet 30 without being folded back. Is the upper side of the page.

  Further, in the present specification, the terms “sheet”, “film”, and “plate” are not distinguished from each other only based on the difference in names.

  Further, in the present specification, the “sheet surface (film surface, plate surface)” is a plane (expansion of the target sheet-like member when the target sheet-like member is viewed globally and globally. ) Refers to the surface that matches the direction. On the surface of the optical sheet 30 on which the unit lenses 35 are arranged, the envelope surface of the surface of the plurality of unit lenses 35 is the sheet surface. In the present embodiment, the image forming surface (light exit surface) 15a of the image forming apparatus 15, the sheet surface of the optical sheet 30, the sheet surface of the main body 32 of the optical sheet 30 described later, and the main body 32 of the optical sheet 30 described later. The light incident side surface, the light exit side surface 32a of the main body 32 of the optical sheet 30 to be described later, the display surface 10a of the image display device 10 and the like are parallel to each other.

  Furthermore, terms used in the present specification for specifying shapes and geometric conditions, for example, terms such as “parallel”, “orthogonal”, “ellipse”, “circle”, and the like are not restricted to a strict meaning. Therefore, it should be interpreted including an allowable error to the extent that a similar function can be expected.

  Next, the optical sheet 30 will be described in detail. As shown in FIG. 2, the optical sheet 30 includes a sheet-like main body portion 32 and a large number of unit lenses 35 arranged on the main body portion 32. The optical sheet 30 changes the traveling direction of the image light from the image forming apparatus 15 by refraction or reflection at the unit lens 35. In the illustrated example, the unit lens 35 is provided on the light output side surface 32 a of the main body 32, and forms the light output surface 30 a of the optical sheet 30 and the display surface 10 a of the image display device 10. The main body 32 is a part that supports the unit lens 35 and is appropriately configured so as to have appropriate strength and appropriate transparency. As an example, the thickness of the main body 32 can be set to 20 μm to 200 μm.

  As shown in FIG. 2, the unit lenses 35 are two-dimensionally arranged on the light output side surface 32a of the main body 32, and constitute microlenses or eyelid lenses (fly eye lenses). That is, the unit lenses 35 are arranged on the light output side surface 32a of the main body 32 so as to be spread on a plane, not arranged in only a single direction. In the present embodiment, as shown in FIGS. 2 and 3, a large number of unit lenses 35 are arranged adjacent to each other on the light output side surface 32 a of the main body 32 without a gap. Therefore, the light exit surface 30 a of the optical sheet 30 that forms the display surface 10 a of the image display device 10 is formed only by the lens surface of the unit lens 35.

  As shown in FIGS. 5 and 6, when the optical sheet 30 is observed from the normal direction to the sheet surface of the optical sheet 30 (vertical direction in FIGS. 1 and 2), the sheet surface of the optical sheet 30 The array pattern 40 is specified by the outer contour (outer edge) of the unit lens 35 along the line. The array pattern 40 is formed from a large number of boundary line segments 48 extending between two branch points 46 and defining a closed region 42, and one unit lens 35 is provided in one closed region 42 of the array pattern 40. Will be placed. As shown in FIGS. 5 and 6, the shape or area of many closed regions 42 included in the array pattern 40 is not constant. As a result, the shape of the bottom surface on the light output side surface 32 a of the main body 32 is not constant among the many unit lenses 35 included in the optical sheet 30. The arrangement pattern 40 of the unit lenses 35 will be described in detail later.

  FIG. 3 is a cross-sectional view along the normal direction to the sheet surface of the optical sheet 30 shown in FIG. The cross-sectional shape of the unit lens 35 is appropriately designed according to the optical function expected for the optical sheet 30. In the example shown in FIG. 3, the unit lens 35 is a convex lens, and the unit lens 30 is configured to exhibit a light diffusion function for diffusing transmitted light. For example, when the image forming apparatus 10 is a liquid crystal display panel, generally, video light emitted from the liquid crystal display panel is collected to some extent in the front direction. According to the combination of such a liquid crystal display panel and the optical sheet 30 having a light diffusion function, a wide viewing angle can be given to the image display device 10. As a specific configuration, by setting the radius of curvature of the light exit surface 30 a of the unit lens 35 to be small, specifically, the angle θa formed by the light exit surface of the unit lens 35 with respect to the sheet surface of the optical sheet 30 is reduced. By setting or by setting a ratio (Ha / Wa) of the height Ha to the width Wa of the unit lens 35 to be small, the unit lens 35 is condensed relatively in the front direction. There tends to be a light diffusing function for light.

  In the example shown in FIGS. 2 and 3, the light exit surface (lens surface) of the unit lens 35 is formed as a curved surface. Therefore, as shown in FIG. 2, in the cross section along the normal direction to the sheet surface of the optical sheet 30, the light exit surface (lens surface) of the unit lens 35 is approximated by an arc, an elliptical arc, or an arc connection. It becomes a curved line. In the unit lens 35 configured by a curved surface, an angle θa formed by the light exit surface of the unit lens 35 with respect to the sheet surface of the optical sheet 30 is a tangent to the unit lens 35 in a cross section along the normal direction of the optical sheet 30. The TL is specified as an angle formed with respect to the sheet surface of the optical sheet 30.

  FIG. 4 shows another example of the cross-sectional shape of the unit lens 35. In the unit lens 35 shown in FIG. 4, by setting the radius of curvature of the light exit surface 30a of the unit lens 35 larger than that of the unit lens shown in FIG. The angle θa formed by the light exit surface with respect to the sheet surface of the optical sheet 30 is set large, and the ratio of the height Ha to the width Wa of the unit lens 35 (Ha / Wa) is set large. As shown in FIG. 4, when light traveling in a direction inclined relatively from the front direction is incident on the optical sheet 30, the unit lens 35 of the optical sheet 30 exhibits a condensing function, and The traveling direction is deflected in the front direction. In the example shown in FIG. 4, the cross-sectional shape of the unit lens 35 is a triangular shape or a shape formed by chamfering one or more corners of a triangle, in particular, a right isosceles triangular shape arranged symmetrically about the front direction. Alternatively, it has a shape formed by chamfering one or more corners of a right-angled isosceles triangle, and can exhibit an extremely excellent light collecting function.

  The optical sheet 30 as described above is formed by molding the unit lens 35 on a resin layer laminated on a base film made of, for example, a biaxially stretched polyethylene terephthalate (PET) film as the main body portion 32. Can be made. As the resin for forming the unit lens 35, for example, an epoxy acrylate prepolymer having a characteristic of being cured by ionizing radiation such as an electron beam or ultraviolet rays can be used. As another manufacturing method, the optical sheet 30 can be produced by melt extrusion molding or injection molding using a thermoplastic resin such as polycarbonate.

  Note that the dimensions of the unit lens 35 can be appropriately determined in consideration of the optical function expected of the unit lens 35 as described above. However, the minimum width of the unit lens 35 needs to be equal to or greater than the maximum wavelength (800 nm) of visible light so that it can effectively exert an optical action on visible light. It is preferable that it is 10 micrometers or more. On the other hand, when the width Wa of the unit lens 35 becomes too large, the individual unit lenses 35 are visually recognized, and the image quality of the display image is deteriorated. From this point, it is preferable that the maximum width of the unit lens 35 is 300 μm or less.

  Next, the arrangement pattern 40 of the unit lenses 35 of the optical sheet 30 will be described with reference mainly to FIGS.

  As shown in FIGS. 5 and 6, the line portion 44 is specified on one surface 32 a of the main body portion 32 corresponding to the array pattern 40 of the unit lenses 35 in the sheet surface of the optical sheet 30. More specifically, the line portion 44 is defined on the one surface 32 a of the main body portion 32 so as to extend between two adjacent unit lenses 35. In other words, as shown in FIGS. 5 and 6, the outer contour of the unit lens 35 having translucency can be specified on the one surface 32 a of the main body 32 by the line portion 44. Hereinafter, the arrangement pattern 40 of the unit lenses 35 will be described using the line portion 44.

  As shown in FIGS. 5 and 6, the line portion 44 has a mesh shape that defines a large number of closed regions 42. One unit lens 35 is arranged in one closed region 42. As described above, in the optical sheet 30 according to the present embodiment, the unit lens 35 is disposed on the one surface 32a of the main body 32 so as to be in contact with no gap. Therefore, as shown in FIGS. 5 and 6, the line portion 44 that specifies the arrangement pattern 40 of the unit lenses 35 is along the boundary (valley portion) between the adjacent unit lenses 35, in other words, the optical sheet 30. It extends along the outer edge (outer contour) of the unit lens 35 along the sheet surface. As a result, when the optical sheet 30 is observed from the normal direction, the line portion 44 can be visualized as representing the outer contour of the unit lens 35 or the arrangement pattern 40 of the unit lens 35.

  As shown in FIGS. 5 and 6, the line portion 44 that specifies the arrangement pattern 40 of the unit lenses 35 is formed in a net shape and includes a large number of branch points 46. The line portion 44 that specifies the array pattern 40 is composed of a number of boundary line segments 48 that form branch points 46 at both ends. That is, the line portion 44 that specifies the arrangement pattern 40 is composed of a number of boundary line segments 48 extending between the two branch points 46. A closed region 42 is defined by connecting a boundary line segment 48 at the branch point 46. In other words, one closed region 42 is defined by being surrounded and bounded by the boundary line segment 48.

  As shown in FIGS. 5 and 6, since the line portion 44 is constituted only by the boundary line segment 48, there is no line portion 44 that extends into the closed region 42 and becomes a dead end. According to this aspect, the outer contour of the unit lens 35 has a circumferential shape, and no cuts or dents that cause bright spots or defects are formed on the outer surface (lens surface) of the unit lens 35.

  Further, as described above, the dimension of the unit lens 35 can be appropriately determined in consideration of the optical function expected for the unit lens 35. However, the minimum width of the unit lens 35 needs to be equal to or greater than the maximum wavelength (800 nm) of visible light so that it can effectively exert an optical action on visible light. It is preferable that it is 10 micrometers or more. On the other hand, when the width Wa of the unit lens 35 becomes too large, the individual unit lenses 35 are visually recognized, and the image quality of the display image is deteriorated. From this point, it is preferable that the maximum width of the unit lens 35 is 300 μm or less.

  From the viewpoint of setting the minimum width of the unit lens 35 to 10 μm or more, two arbitrarily selected branch points 46 among the three or more branch points 46 forming one closed region 42 are formed on the main body 32. Are preferably separated by a distance of 10 μm or more. In other words, it is preferable that two closest branching points 46 among the three or more branching points 46 forming one closed region 42 are separated by 10 μm or more on the main body 32. Further, from the viewpoint of setting the maximum width of the unit lens 35 to 300 μm or less, two arbitrarily selected branch points 46 among the three or more branch points 46 forming one closed region 42 are formed on the main body 32. Are preferably separated by a distance of 300 μm or less. In other words, the distance between the two most distant branch points 46 among the three or more branch points 46 forming one closed region 42 is preferably 300 μm or less on the main body 32.

  By the way, as described above, when an optical sheet including unit lenses arranged in a predetermined arrangement pattern is arranged on the image forming apparatus, it is caused by interference between the periodicity of the arrangement pattern of unit lenses and the periodicity of the pixel arrangement. Striped patterns, that is, moire (interference fringes) may be visually recognized. When the moiré is visually recognized, the image quality of the image displayed on the image display device is significantly deteriorated.

  Here, FIG. 17 shows a conventional typical microlens array sheet (fly-eye lens sheet) 130 having a square lattice-like arrangement pattern 140. 19 shows a microlens array sheet 130 in which unit lenses are arranged in the conventional arrangement pattern 140 shown in FIG. 17 on the image forming apparatus 15 having a typical pixel arrangement shown in FIG. The arranged state is shown. FIG. 18 shows a conventional typical microlens array sheet (fly-eye lens sheet) 230 having a honeycomb-shaped arrangement pattern 240 in which regular hexagons are regularly arranged. 20 shows a microlens array sheet 230 in which unit lenses are arranged in the conventional arrangement pattern 240 shown in FIG. 18 on the image forming apparatus 15 having a typical pixel arrangement shown in FIG. The arranged state is shown. As shown in FIG. 19 and FIG. 20, when the square lens-like or honeycomb-like arrangement patterns 140 and 240 of the unit lenses and the typical pixel arrangement of the image forming apparatus are overlaid, the arrangement patterns 140 and Due to the interference between the regularity (periodicity) 240 and the regularity (periodicity) of the pixel arrangement, light and dark stripes are visually recognized.

  On the other hand, in order to prevent the occurrence of moiré, the line portion 44 corresponding to the array pattern 40 of the unit lenses 35 according to the present embodiment has closed regions 42 and 6 surrounded by five boundary segments 48. A plurality of at least two types selected from the closed region 42 surrounded by the boundary line segment 48 and the closed region 42 surrounded by the seven boundary line segments 48 are included. In addition, the line portion 44 corresponding to the array pattern 40 of the unit lenses 35 according to the present embodiment is surrounded by the same number of boundary line segments 48 out of 5, 6, or 7 included in the array pattern 40. The shape or area of the plurality of closed regions 42 surrounded by (the area of the portion surrounded by the boundary line segment) is not constant. That is, if the line portion 44 includes a plurality of closed regions 42 (corresponding to a pentagon when the closed region is a polygon) surrounded by five boundary line segments 48, At least two of the plurality of closed regions 42 defined by the boundary line segments 48 have different shapes or areas, and the plurality of closed regions 42 surrounded by the six boundary line segments 48 are formed in the line portion 44. If included, at least two of the plurality of closed regions 42 defined by the six boundary segments 48 have different shapes or areas, and are further surrounded by the seven boundary segments 48. When the plurality of closed regions 42 are included in the line portion 44, at least two of the plurality of closed regions 42 defined by the seven boundary line segments 48 have different shapes or areas. . According to such an aspect, the arrangement pattern 40 of the unit lenses 35 defined by the line portion 44 can be effectively irregularized.

  Here, the fact that at least two of the closed regions 42 have different shapes or areas means that (a) when at least two of the fully closed regions have different shapes and the fully closed regions have the same area, b) When at least two of the fully closed regions have different areas and the fully closed regions have the same shape, (c) the fully closed region has the same shape and the fully closed region has the same area. Means that it falls under either case. More preferably, 50% or more of the plurality of closed regions 42 surrounded by the same number of boundary line segments 48 are configured to have different shapes or areas. More preferably, all of the plurality of opening regions 42 surrounded by the same number of boundary line segments 48 are configured to have different shapes or areas. When two (or more) congruent closed regions 42 have different directions, the shapes of the closed regions 42 are different from each other (however, the areas are the same).

  As a result of intensive research, the inventors of the present invention do not simply irregularize the arrangement pattern 40 of the unit lenses 35 defined by the line portion 44, but surround the periphery by five boundary line segments 48. At least two types of a closed region 42, a closed region 42 surrounded by six boundary segments 48, and a closed region 42 surrounded by seven boundary segments 48, each include a plurality of lines. The shape or area of the plurality of closed regions 42 included in the portion 44 and surrounded by the same number of boundary lines 48 out of 5, 6, or 7 included in the line portion 44 is constant. However, by defining the pattern of the line portion 44, the optical sheet 30 having a large number of unit lenses 35 may be generated when the optical sheet 30 is overlaid on the image forming apparatus 15 having a pixel array. It was found that it becomes possible to not very effectively highlight les.

  In general, making a pattern irregular has been considered effective for making moiré invisible. However, according to the studies by the present inventors, in practice, even if the arrangement pattern of the unit lenses is simply made irregular, the moire cannot always be made sufficiently inconspicuous.

  For example, in the conductive mesh disclosed in Japanese Patent Application Laid-Open No. 11-121974, there is no periodicity in the Y-axis direction in the two-dimensional XY plane. Does not have a complete repetition period and can be viewed as an inconsistent pattern. That is, by making the shape or arrangement pitch of the opening area partially irregular, the repeating regularity of the arrangement of the opening area can be specified at a constant repetition pitch in the vertical and horizontal directions. Compared with the square lattice-like arrangement pattern of FIG. 17 arranged in the linear direction, the conductive mesh itself can be visually recognized as an irregular pattern as a whole.

  As a result of confirmation by the present inventors, the unit lens of the above-described dimension example is placed on the main body portion in an arrangement pattern determined by the line portion of the same pattern as the conductive mesh disclosed in Japanese Patent Application Laid-Open No. 11-121974. When the optical sheet was prepared by arranging the unit lenses, the unit lenses were visually recognized as being arranged in an irregular pattern on the main body. However, when this optical sheet is overlapped with the image forming apparatus 15, the occurrence of moiré that can be visually recognized cannot be reliably prevented. The reason why the moire cannot be made inconspicuous effectively is considered to be because it still has a repetition cycle in the X-axis direction. That is, if a partial periodicity remains in any direction in the XY plane even partially, it is considered that moire occurs due to the residual periodicity.

  On the other hand, as in WO 2007/114076, moire can be eliminated if each closed region has a completely irregular pattern in both the X-axis direction and the Y-axis direction in the two-dimensional XY plane. Is also possible. However, when such a completely irregular pattern is adopted, a new problem occurs. That is, because the shape and area of each closed region are not uniform, when the entire conductive mesh is viewed, unevenness in shading is conspicuous in the appearance of the conductive mesh itself. This is a drawback in applications that are installed on the screen of an image display device.

  In the first place, the irregular pattern of the conductive mesh disclosed in WO2007 / 114076 can be realized by a predetermined method of manufacturing the conductive mesh. Therefore, it is impossible to reproduce the irregular pattern disclosed in WO 2007/114076 as the irregular pattern of the unit lens in the optical sheet. Even if it can be reproduced, the shape of some unit lenses may be lost or deformed with respect to the main body design shape, or the unit lens arrangement may be biased. As a result, it is expected that unevenness of shading and in-plane unevenness of optical characteristics will occur.

On the other hand, like the optical sheet 30 according to the present embodiment described here, the line portion 44 specified from the arrangement pattern 40 of the unit lenses 35 satisfies both of the following conditions (A) and (B). When it is satisfied, it becomes possible to effectively prevent the occurrence of moire and also to effectively prevent the occurrence of uneven density.
Condition (A): a closed region 42 surrounded by five boundary line segments 48, a closed region 42 surrounded by six boundary line segments 48, and seven boundary line segments 48. A plurality of at least two types selected from the enclosed closed region 42 are included in the line portion 44.
Condition (B): The shape or area of the plurality of closed regions 42 surrounded by the same number of boundary lines 48 out of 5, 6, or 7 is not constant. That is, when the line portion 44 includes a plurality of closed regions 42 surrounded by the five boundary line segments 48, the plurality of closed regions defined by the five boundary line segments 48 are included. If at least two of 42 have different shapes or areas and a plurality of closed regions 42 surrounded by six boundary segments 48 are included in the line portion 44, the six boundaries At least two of the plurality of closed regions 42 defined by the line segment 48 have different shapes or areas, and the plurality of closed regions 42 surrounded by the seven boundary line segments 48 include the line portion 44. Are included, the at least two of the plurality of closed regions 42 defined by the seven boundary line segments 48 have different shapes or areas.

  The effect produced by the arrangement pattern 40 of the unit lenses 35 defined corresponding to the line portions 44 satisfying the conditions (A) and (B) is simply to make the pattern irregular as invisible moire. It can be said that this is a remarkable effect that exceeds the range that can be predicted in light of the conventional state of the art. Details of the reason why such an effect is obtained by the array pattern 40 of the unit lenses 35 specified by the line portion 44 that satisfies the conditions (A) and (B) are unknown, but Is presumed to be the reason. However, the present invention is not limited to the following estimation.

  First, according to the condition (A), the arrangement of the closed regions 42 is an arrangement in which regular shapes of the closed regions 42 and the regularity of the arrangement are broken from a honeycomb arrangement in which regular hexagons having the same shape are regularly arranged. In other words, it is possible to obtain an arrangement in which the shape and arrangement of each closed region 42 are randomized with reference to the honeycomb arrangement. As a result, it is possible to suppress the occurrence of apparent roughness in the arrangement of the closed regions 42, and it is estimated that a large number of closed regions 42 can be distributed at a substantially uniform density, that is, approximately uniformly. The In addition, according to the condition (B), the arrangement of a large number of closed regions 42 can be sufficiently randomized. From these facts, it is presumed that both shading unevenness and moire can be effectively made inconspicuous.

  When the inventors of the present invention actually conducted extensive investigations, the arrangement of the closed region 42 was sufficiently randomized when the conditions (A) and (B) were satisfied. Furthermore, when the conditions (A) and (B) are satisfied, the arrangement of the closed regions 42 can be made completely irregular, that is, there can be no direction in which the closed regions 42 are regularly arranged. As a result, it has been confirmed that both density unevenness and moire can be made extremely inconspicuous.

Here, FIG. 6 is a plan view for explaining a state in which there is no direction in which the closed regions 42 are regularly arranged, in other words, a state in which there is no direction in which the closed regions A are arranged with regularity. It is. In Figure 6, the line portion corresponding to the arrangement pattern of the unit lens, a virtual straight line d _i of one facing any direction is selected at an arbitrary position. This one straight line d _i intersects with the boundary line segment 48 of the line portion to form an intersection. The intersections are shown as intersections C ₁ , C ₂ , C ₃ ,..., C _{9 in} order from the lower left side of the drawing. Adjacent intersections, for example, the distance between the intersection C ₁ and the intersection C ₂ is the is the dimension T ₁ of the on linear d _i of one closed region 42 certain. Next, another closed region 42 adjacent along the straight line d _i with respect to closed area 42 having dimensions T ₁ likewise, is determined dimension T ₂ of the on linear d _i. Then, the linear d _i any direction at any position, from the boundary line 48. intersecting the straight line d _i, for a number of the closed region 42 of encountering any direction of linear d _i at an arbitrary position, on the straight line d _i T ₁ , T ₂ , T ₃ ,..., T ₈ are determined. And the arrangement of the numerical values of T ₁ , T ₂ , T ₃ ,..., T ₈ has no periodicity (regularity). That is, the closed regions 42 are arranged so as not to have regularity along the linear direction d _i ,
T _k ≠ T _{k + 1} (k: arbitrary natural number, l: arbitrary natural number) Conditional expression (x)
It comes to satisfy. In FIG. 6, the _{T 1, T 2, T 3} , ······, T 8 is the drawing down as easily understand, separate from the arrangement pattern of the unit lens with linear _{d i} drew It is.

Further, when this straight line d _i is rotated by an arbitrary angle from that shown in FIG. 6 to determine the dimensions T ₁ , T ₂ ,... Of each closed region 42 in another direction, it is also shown in FIG. As in the case, the conditional expression (x) is satisfied also in the direction of the straight line d _{i + 1} , and no repetitive periodicity (regularity) is observed in the dimensions T ₁ , T ₂ ,. Thus, when the closed region 42 satisfies the conditional expression (x) in any direction, there is no direction in which the closed region is regularly arranged, or there is a direction in which the closed region 42 has a repeating cycle. Or the arrangement of the closed region 42 is expressed as having no regularity.

In addition, when the present inventors have investigated the arrangement patterns of various unit lenses, the line portion 44 corresponding to the arrangement pattern 40 of the unit lenses 35 has the following in addition to the conditions (A) and (B): When the condition (C) is further satisfied, particularly when the conditions (C) and (D) are further satisfied, both the uneven density and the moire can be made less noticeable. Further, when the line portion 44 that specifies the arrangement pattern 40 of the unit lenses 35 further satisfies the following conditions (C), (D), and (E) in addition to the conditions (A) and (B): In addition, both the shading unevenness and the moire could be made inconspicuous. Such a tendency agrees with the above estimation and can be said to be a phenomenon that supports the above estimation.
Condition (C): A plurality of closed regions 42 surrounded by six boundary line segments 48 are included.
Condition (D): The closed region 42 surrounded by the six boundary line segments 48 is most often included. That is, the closed region 42 surrounded by the six boundary line segments 48 is included more than the closed region 42 surrounded by the other boundary line segments 48.
Condition (E): Let N _{k be} the number of closed regions 42 surrounded by k boundary line segments 48.
When k is an integer satisfying 3 ≦ k ≦ 5, N _k ≦ N _{k + 1}
When k is an integer satisfying 6 ≦ k, N _k ≧ N _{k + 1}
It has become. That is, the closed region 42 surrounded most by the six boundary line segments 48 is included most, and as the number of boundary line segments 48 surrounding the closed region 42 increases from six, the closed region 42 As the number of boundary line segments 48 surrounding the region decreases from six, the number of closed regions 42 decreases.

  Strictly speaking, whether or not the line portion 44 specifying the array pattern 40 of the unit lenses 35 satisfies the conditions (A) to (E) is within the line portion 44 corresponding to the array pattern 40 of the unit lenses 35. Will be investigated for all closed regions 42 included. However, in practice, the overall tendency of the number of boundary line segments 48 surrounding one closed region 42 is considered in consideration of the size of each closed region 42 defined by the line portion 44. Enclose the closed region 42 included in one section having an area expected to reflect (for example, a portion of 30 mm × 30 mm in the line portion 44 in which the closed region 42 is formed in the dimension example described above). The number of boundary line segments 48 may be examined to determine whether or not each condition (A) to (E) is satisfied. Similarly, whether or not the closed region 42 has a regularly arranged direction exists, strictly speaking, in any region in the line portion 44 corresponding to the array pattern 40 of the target unit lenses 35. We will investigate the sequence of closed regions in the direction of. However, in practice, a section having an area expected to reflect the overall tendency of the arrangement of the closed regions 42 (for example, in the arrangement pattern in which the closed regions 42 are formed in the above-described dimension example). , 30 mm × 30 mm portion) in each direction (for example, in the arrangement pattern in which the closed region 42 is formed in the above-described dimension example, the direction of every 15 °) is examined. Then, it may be determined whether or not the closed region is in a regularly arranged direction.

  Actually, when the line portion 44 for specifying the arrangement pattern 40 of the unit lenses 35 shown in FIG. 5 was investigated, as shown in FIG. 7, the line portion 44 has four, five, six, There were 79, 1141, 2382, 927, 94, and 8 closed regions 42 surrounded by seven, eight, and nine boundary segments 48, respectively. Further, the line portion 44 did not include the closed region 42 surrounded by three boundary line segments 48 and the closed region 42 surrounded by ten or more boundary line segments 48. That is, the line portion 44 corresponding to the arrangement pattern 40 of the unit lenses 35 shown in FIG. 5 satisfies the conditions (C), (D), and (E) in addition to the conditions (A) and (B). Yes.

  9 shows a state in which the optical sheet 30 in which unit lenses are arranged in the arrangement pattern 40 shown in FIG. 5 is arranged on the image forming apparatus 15 having a typical pixel arrangement shown in FIG. It is shown. As can be understood from FIG. 9, when the optical sheet 30 in which the unit lenses are arranged in the arrangement pattern 40 shown in FIG. 5 is actually produced and arranged on the pixel arrangement of the image forming apparatus 15, it is visually recognized. A striped pattern, that is, a moire pattern (interference fringe) was not generated.

In addition, as a result of repeated researches by the present inventors, the line portion 44 specified from the arrangement pattern 40 of the unit lenses 35 also satisfies the following condition (F) in order to make both unevenness of darkness and moire more inconspicuous. The regular shape of each closed region 42 and the regularity of the arrangement are broken from the honeycomb arrangement in which regular hexagons having the same shape are regularly arranged or from the square lattice arrangement in which squares are regularly arranged. The arrangement, in other words, the arrangement and the arrangement of the closed regions 42 can be randomized with reference to the honeycomb arrangement or the square lattice arrangement.
Condition (F): It has been found that it is effective that the average number of boundary line segments 48 extending from one branch point 46 is 3.0 or more and less than 4.0. The average number of boundary line segments 48 extending from one branch point 46 is 3.0 or more and less than 4.0.
As a result, it is possible to suppress the occurrence of apparent roughness in the arrangement of the closed regions 42, and it is estimated that a large number of closed regions 42 can be distributed at a substantially uniform density, that is, approximately uniformly. The Actually, as a result of extensive research conducted by the present inventors, when the average number of boundary line segments 48 extending from one branch point 46 is 3.0 or more and less than 4.0, the arrangement of the closed regions 42 is determined. It is possible to stably make the closed region 42 not to have a direction in which the closed regions 42 are arranged with repeating regularity (periodicity), and as a result, moire is very effectively inconspicuous. It was confirmed that it would be possible. Actually, when the line portion 44 corresponding to the unit lens array pattern 40 shown in FIG. 5 was investigated, the average number of branches at one branch point was 3.08, which was larger than 3. It was 3.1 or less.

  Strictly speaking, the average number of boundary line segments 48 extending from one branch point 46 extends for all branch points 46 included in the line portion 44 corresponding to the array pattern 40 of the unit lenses 35. The average value is calculated by examining the number of the boundary line segments 48. However, in actuality, the size of the closed region 42 per line defined by the line portion 44 is taken into consideration. A section having an area expected to reflect the overall tendency of the number of boundary line segments 48 extending from one branch point 46 (for example, an array in which the closed region 42 is formed in the above-described dimension example) In the pattern, the number of boundary line segments 48 extending with respect to the branch point 46 included in the 30 mm × 30 mm portion) is examined to calculate the average value, and the calculated value is used as the array pattern 40 of the unit lenses 35. Corresponding One may be treated as the average value of the number of boundary segments 48 extending out from the branch point 46 of the in-44.

  Here, an example of a method for producing the pattern of the line portion 44 (the arrangement pattern of the unit lenses 35) that satisfies the above-described conditions (A) and (B) will be described. In other words, the optical sheet 30 first determines the pattern of the line portion 44, and then forms the unit lens 35 on the main body portion 32 in accordance with the arrangement pattern 40 specified by the determined line portion 44. In addition, one unit lens 35 may be arranged in each closed region 42 defined by the determined line portion 44.

  Note that the pattern of the line portion 44 shown in FIG. 5 described above is a pattern actually determined by the method described below. As already described, the produced line portion 44 satisfies not only the conditions (A) and (B) but also the conditions (C), (D), and (E). The average number of extending boundary line segments 48 was 3.0 or more and less than 4.0, and the condition (F) was also satisfied.

  The method described below includes a step of determining a generating point, a step of creating a Voronoi diagram from the determined generating point, and a boundary segment extending between two Voronoi points connected by one Voronoi boundary in the Voronoi diagram. And determining the pattern of the line portion 44 by determining the thickness of the determined path to demarcate each boundary line segment. Hereinafter, each step will be described in order.

  First, the process of determining a generating point will be described. First, as shown in FIG. 10, a first generating point (hereinafter referred to as “first generating point”) BP1 is arranged at an arbitrary position in the absolute coordinate system OXY. The absolute coordinate system referred to here is a normal two-dimensional space (plane), but is particularly called an absolute coordinate system in order to distinguish it from a relative coordinate system described later. Next, as shown in FIG. 11, the second generating point BP2 is arranged at an arbitrary position away from the first generating point BP1 by a distance r1 or more and a distance r2 or less. That is, the circumference of the radius r1 located on the absolute coordinate system XY around the first generating point BP1, the circumference of the radius r2 located on the absolute coordinate system XY around the first generating point BP1, The second generating point BP2 is arranged in an annular region surrounded by. Here, the distance r1 is smaller than the distance r2 (r1 <r2), and when the line portion 44 shown in FIG. 5 is manufactured, the distance r1 is 160 μm and the distance r2 is 190 μm.

  Next, as shown in FIG. 12, the third mother point BP1 is separated from the first mother point BP1 by a distance r1 or more and a distance r2 or less, and is further separated from the second mother point BP2 by a distance r1 or more. Point BP3 is arranged. Thereafter, the fourth generating point is arranged at an arbitrary position away from the first generating point BP1 by the distance r1 or more and the distance r2 or less and further from the other generating points BP2 and BP3 by the distance r1 or more. In this way, until the next generating point cannot be arranged, it is separated from the first generating point BP1 by the distance r1 or more and the distance r2 or less, and in addition, the distance from the other generating points BP2, BP3,. The mother point is arranged at an arbitrary position separated by r1 or more. That is, the circumference of the radius r1 located on the absolute coordinate system XY around the first generating point BP1, the circumference of the radius r2 located on the absolute coordinate system XY around the first generating point BP1, The mother points are arranged until there is no position apart from the mother point except the first mother point BP1 by the distance r1 or more in the annular region surrounded by.

  Thereafter, this operation is continued based on the second generating point BP2. That is, it is separated from the second generating point BP2 by a distance r1 or more and a distance r2 or less, and further at an arbitrary position distant from the other generating points BP1, BP3, BP4,. Place the mother point. With reference to the second generating point BP2, until the next generating point cannot be arranged, that is, with the circumference of the radius r1 positioned on the absolute coordinate system XY with the second generating point BP2 as the center, In the annular area surrounded by the circumference of the radius r2 located on the absolute coordinate system XY with the second generating point BP2 as the center, the distance r1 or more from all generating points other than the second generating point BP2 The mother point is arranged until there is no remote position. Thereafter, the base point as a reference is sequentially changed, and the base point is formed in the same procedure.

  With the above procedure, the mother point is arranged until the mother point cannot be arranged in the region where the line portion 44 (array pattern 40) is to be determined, in other words, in the region where the unit lens 35 is to be arranged. I will do it. When the generating point cannot be arranged in the region where the line portion 44 is to be formed, the generating step of the generating point is completed. By the processing so far, the generating point groups irregularly arranged on the two-dimensional plane (XY plane) are uniformly dispersed in the region where the array pattern 40 is to be formed.

With respect to the generating point groups BP1, BP2,..., BP6 (see FIG. 13A) distributed in the two-dimensional plane (XY plane) in such a process, the distances between the individual generating points are not constant. Have a distribution. However, the range between any distribution completely random distribution of distances between two adjacent base points (uniformly distributed) but without the upper limit value R _MAX and the lower limit value R _MIN across the mean value R _AVG [Delta] R = It is distributed in R _MAX -R _MIN . Here, regarding two adjacent generating points, when a Voronoi diagram is created as described later from the generating point groups BP1, BP2,... It is defined that the generating points located in the two Voronoi regions XA are adjacent to each other. In FIG. 13A, a Voronoi boundary (see FIG. 14) obtained from these generating point groups is shown by a broken line for reference.

That is, with respect to the generating point group described here, a coordinate system having each generating point as an origin (referred to as a relative coordinate system oxy), on the other hand, an actual two-dimensional plane (coordinate system) is absolute as described above. 13 (B), FIG. 13 (C),... In which all the generating points adjacent to the generating point placed on the origin are plotted on the coordinate system O-XY). Find the mother point. Then, when the graphs of the adjacent generating points on all the relative coordinate systems are displayed with the origin o of each relative coordinate system superimposed, a graph as shown in FIG. 13D is obtained. The distribution pattern of adjacent mother point groups on such a relative coordinate system is such that the distance between any two adjacent mother points constituting the mother point group is not a uniform distribution from 0 to infinity, but more than zero. It is distributed within a finite range from a large (R _AVG -ΔR) to (R _AVG + ΔR) (a donut-shaped region from a radius R _MIN to R _MAX ).

In this way, a restriction is imposed on the distance between adjacent two generating points, while no restriction is imposed on the directionality of generating points. For this reason, as shown in FIG. 13D, the distribution pattern in the azimuth direction of the adjacent generating point group on the relative coordinate system (in the curved coordinate system rθ, the θ coordinate direction) is uniform and irregular. And isotropically distributed within a donut-shaped region from radius R _MIN to R _MAX .

  By setting the distance between each generating point in this way, the Voronoi region XA obtained from the generating point group by the method described below, and the distribution of the area of the closed region 42 obtained therefrom are also uniform. It is not distributed (completely random) but distributed within a finite range. As a result, the surface distribution of transparency when the unit lenses 35 arranged in the arrangement pattern 40 corresponding to the produced line portion 44 are visually observed becomes more uniform.

In addition, from the viewpoint of making the shading unevenness that is generated when the size and arrangement of the unit lenses 35 are biased substantially invisible, and securing the moire prevention due to the non-periodicity of the arrangement of the unit lenses 35, The value of the ratio of ΔR (= R _MAX −R _MIN ) to R _AVG (= (R _MAX + R _MIN ) / 2) in the distribution pattern of adjacent generating points on the relative coordinate system shown in FIG. However, it is preferable that it is larger than 0 and 0.6 or less, and it is more preferable that it is 0.2 or more and 0.4 or less. That is, it is preferable that the following condition (y1) is satisfied, and it is more preferable that the condition (y2) is satisfied. When the present inventors formed various patterns and tried them, when the condition (y1) is satisfied, in the normal observation ability, there is no unevenness in density, and when the condition (y2) is further satisfied Even if we observed carefully, we did not feel any shading unevenness.
0 <(ΔR / R _AVG) ≦ 0.6 Condition (y1)
0.2 ≦ (ΔR / R _AVG ) ≦ 0.4 Condition (y2)

In the step of determining the above mother point, by varying the magnitude of the distance r1 and the distance r2, to regulate the size of the closed region 42 of R _AVG and per one in FIG. 13 (D) it can. Specifically, by reducing the size of the distance r1 and the distance r2, RAVG in FIG. _13D can be reduced, and the size of each closed region 42 can be reduced. Conversely, by increasing the size of the distance r1 and the distance r2, RAVG in FIG. _13D can be increased and the size of each closed region 42 can be increased. Further, by changing the difference between the distance r1 and the distance r2, the size of the range in which the distance between two adjacent generating points is dispersed (the size of ΔR in FIG. 13D) can be changed. Specifically, by reducing the difference between the distance r1 and the distance r2, the distance variation ΔR between the two adjacent generating points tends to be reduced.

  Next, as shown in FIG. 14, a Voronoi diagram is created on the basis of the arranged generating points. As shown in FIG. 14, a Voronoi diagram is a diagram composed of line segments that are drawn at the intersection of two perpendicular bisectors by drawing a perpendicular bisector between two adjacent generating points. is there. Here, the line segment of the perpendicular bisector is called a Voronoi boundary XB, the intersection of the Voronoi boundaries XB forming the ends of the Voronoi boundary XB is called a Voronoi point XP, and a region surrounded by the Voronoi boundary XB is a Voronoi region Called XA.

  In the Voronoi diagram created as shown in FIG. 14, each Voronoi point XP forms a branch point 46 of the line portion 44. Then, one boundary line segment 48 is provided between two Voronoi points XP forming the end of one Voronoi boundary XB. At this time, the boundary line segment 48 may be determined so as to extend linearly between the two Voronoi points XP as in the examples shown in FIGS. 5 and 6, or another boundary line segment. Various paths (for example, circle (arc), ellipse (arc), fence line, hyperbola, sine curve, hyperbolic sine curve, elliptic function curve, Bessel function curve, etc.) between two Voronoi points XP within a range not contacting 48 It may be extended in a curved path, a broken line, or the like (a linear path formed by combining a curved line and a straight line). When the boundary line segment 48 is determined to connect the Voronoi points XP in a straight line as in the examples shown in FIGS. 5 and 6, each Voronoi boundary XB defines the boundary line segment 48. Will be completed.

  After determining the path of each boundary line segment 48, the line width (thickness) of each boundary line segment 48 is determined. The line width of the boundary line segment 48 is, for example, such that the aperture ratio is in the above-described range, that is, the unit lens 35 can exhibit an optical function with respect to visible light, and each unit lens 35 Is determined so as not to be visually recognized. As described above, the pattern of the line portion 44 for determining the arrangement pattern 40 of the unit lenses 35 can be produced. The line width of the boundary line segment 48 is usually set in the range of 0 μm to 100 μm.

  According to the present embodiment as described above, the line portion 44 including the boundary line segment 48 extending between the unit lenses 35 is specified on one surface of the main body portion according to the arrangement pattern 40 of the unit lenses 35. Is done. The boundary line segment 48 extends between the two branch points 46 to define a closed region 42, and one unit lens 35 is disposed in one closed region 42 of the line portion 44. Are arranged on one surface 32 a of the main body 32. The array pattern 40 of the optical sheet 30 is formed by a number of boundary line segments 48 extending between the two branch points 46 and defining the closed region 42, and is surrounded by the five boundary line segments 48. At least two types selected from the closed region 42, the closed region 42 surrounded by the six boundary line segments 48, and the closed region 42 surrounded by the seven boundary line segments 48 are line portions. And the shape or area of the plurality of closed regions 42 surrounded by the same number of boundary line segments 48 out of 5, 6, or 7 formed by the line portion 44. It is not constant. As a result, even if this optical sheet 30 is superimposed on the image forming apparatus 15 in which the pixels P are regularly (periodically) arranged, the stripe-like pattern (moire, interference fringe) is generated to such a degree that it can be visually recognized. This can be effectively prevented.

  Note that various modifications can be made to the above-described embodiment.

  For example, in the above-described embodiment, the example in which the boundary line segment 48 of the line portion 44 is formed in a straight line is shown, but the present invention is not limited thereto. As described above, the boundary line segment 48 may extend between the two branch points 46 along various paths such as a curved line.

  Furthermore, the pattern design method of the line part 44 mentioned above is only an example. For example, the mother point may be arranged in the following procedure. First, as in FIG. 10, the first generating point BP1 is arranged at an arbitrary position in the absolute coordinate system XY. Next, the second mother BP2 is arranged at an arbitrary position separated from the first mother point BP1 by the distance r. Thereafter, the third mother point BP3 is arranged at an arbitrary position separated from the first mother point BP1 by the distance r and further away from the second mother point BP2 by the distance r or more. Thereafter, the next mother point is sequentially placed at an arbitrary position away from the first mother point BP1 by the distance r and at any position away from all the mother points BP2 and BP3 other than the first mother point BP1 that has already been arranged. Place it. If it becomes impossible to arrange the mother point at the position separated from the first mother point BP1 by the distance r by the above procedure, then the second mother point is separated from the second mother point by the distance r and is already arranged. The next generating points are arranged in order at an arbitrary position at a distance r or more from all generating points other than the generating point BP2. In this way, with the second generating point BP2 as a reference, the generating point is arranged until the next generating point cannot be arranged. Thereafter, the base point as a reference is sequentially changed, and the base point is formed in the same procedure. With the above procedure, the mother point is arranged until the mother point cannot be arranged in the region where the unit lens 35 is to be provided. When the generating point cannot be arranged in the region where the unit lens 35 is to be provided, the step of generating the generating point ends. Even with such a process, irregularly arranged generating point groups can be uniformly dispersed in a region where the unit lenses 35 are to be provided.

  Furthermore, the mother point can be arranged in the following procedure. First, as in FIG. 10, the first generating point BP1 is arranged at an arbitrary position in the absolute coordinate system XY. Next, the second mother BP2 is arranged at an arbitrary position away from the first mother point BP1 by a distance r or more. Thereafter, the third generating point BP3 is arranged at an arbitrary position away from each of the first generating point BP1 and the second generating point BP2 by a distance r or more. Thereafter, the next mother point is sequentially arranged at an arbitrary position separated from the already arranged mother points by a distance r or more. With the above procedure, the mother point is arranged until the mother point cannot be arranged in the region where the unit lens 35 is to be provided. When the generating point cannot be arranged in the region where the unit lens 35 is to be provided, the step of generating the generating point ends. Even with such a process, irregularly arranged generating point groups can be uniformly dispersed in a region where the unit lenses 35 are to be provided.

  Furthermore, in the pattern design method of the line portion 44 for specifying the arrangement pattern 40 of the unit lenses 35 described above, first, a specific generating point is drawn in a plane, and then a line is formed as a Voronoi division pattern of the generating point. Although an example of forming the pattern of the portion 44 has been shown, the present invention is not limited to this. For example, by manually drawing pentagonal and hexagonal closed regions 42 having different sizes and shapes within a plane, and at that time, there is no repetition period in any direction, The pattern of the line portion 44 may be drawn by drawing with care so that the size of the square and hexagon (area to the maximum diagonal length) is within a predetermined range.

  Further, in the above-described embodiment, the example in which the unit lenses 35 are disposed adjacent to each other on the one surface 32a of the main body 32 without a gap is shown, but the present invention is not limited thereto. All or a part of the unit lens 35 may be arranged on the one surface 32 a of the main body 32 so as to be separated from each other. In such a modification, the boundary line segment 48 of the line portion 44 may extend on the one surface 32 a of the main body portion 32 at a position that is equidistant from the two adjacent unit lenses 35. More specifically, the outer contour (outer edge) of the unit lens 35 located on both sides of the boundary line segment 48 from each position of the boundary line segment 48 along the direction orthogonal to the boundary line segment 48 at the position. The distance may be the same. Alternatively, as shown in FIG. 15, the boundary line segment 48 of the line portion 44 extends from the center position CP that is the center in the length direction along the direction orthogonal to the boundary line segment 48 at the center position CP. You may specify so that it may become equidistance to the outer outline (outer edge) of the unit lens 35 located in the both sides of the said boundary line segment 48. FIG. Further, in this modification, the boundary line segment 48 may be configured as a straight line as shown in FIG. 15, may be configured as a curve, or may be configured as a combination of a straight line and a curve. Also good. Even with such an optical sheet 30, both moire and shading unevenness can be effectively made inconspicuous.

  Furthermore, in the above-described embodiment, the above-described conditions (A) and (B) and the conditions (C) to (E) are satisfied in the entire region where the unit lens 35 of the optical sheet 30 is to be disposed. Furthermore, an example is shown in which the condition (F) is also satisfied and there is no direction in which the closed regions 42 of the line portions 44 are arranged with periodicity. However, the conditions (A) and (B) may be satisfied in a part of the region in which the unit lens 35 is to be provided.

  As a typical modification, as shown in FIG. 16, a region satisfying the above-described conditions (A) and (B), preferably a region satisfying the above-described conditions (A) to (E), and further the above-described condition (A ) To (E) and the region (unit pattern region) S in which the closed region 42 is regularly arranged is not provided, or the number of boundary line segments 48 extending from one branch point 46 is prepared. A region having an average of 3.0 or more and less than 4.0, and further, a region (unit pattern region) S that satisfies the condition (F) and does not have a direction in which the closed regions 42 are regularly arranged are prepared. A plurality of the regions S may be aggregated to constitute the entire region where the unit lens 35 is to be provided. That is, in this embodiment, two or more unit pattern regions S in which the closed region groups 42 are arranged in the same pattern are included in the entire region where the unit lens 35 is to be provided.

  In this example, the pattern of the line portion 44 in one region S can be created in the same manner as the pattern creation method described with reference to FIGS. 10 to 14, for example, or according to the above-described modification. It can be created in the same manner as the pattern creation method. Particularly recently, the display surface 10a of the image display device 10 has been increased in size as represented by a plasma display device and a liquid crystal display device. Particularly for such a large-sized image display device, the line portion 44 corresponding to the array pattern 40 of the unit lenses 35 includes a plurality of unit pattern regions S, and each unit pattern region S. In the case where the closed regions 42 are arranged in the same pattern, it is preferable in that the pattern creation of the line portion 44 can be greatly facilitated.

  In the example shown in FIG. 16, the region in which the unit lens 35 of the optical sheet 30 is to be arranged is divided into six unit pattern regions S having the same shape, and the line portion 44 in each region S. Are configured in the same pattern. The six regions S are arranged so that three regions are arranged in the vertical direction of FIG. 16 and two regions are arranged in the horizontal direction of FIG.

  In such a modification, for example, as shown in FIG. 16, the range in which the closed regions 42 of the line portions 44 are arranged in a certain arrangement within the region where the unit lens 35 is to be disposed is the unit pattern region S. As many as the number of the region is repeatedly present in a direction parallel to the arrangement direction of the region. That is, within the region where the unit lens 35 is to be disposed, there is a linear direction in which the plurality of closed regions 42 of the line portion 44 are repeatedly arranged with a predetermined regularity. In this case, due to the regular arrangement of the regions S, there is a concern that striped patterns (moire, interference fringes) or shading unevenness may occur. For this reason, it is preferable that the number of closed regions 42 included in the unit pattern region S is as large as possible in order to make it difficult to visually recognize the repetition of the unit pattern region S.

  However, if the number of repetitions of the same unit pattern region S in a specific direction is suppressed to a certain level, such a striped pattern and shading unevenness can be ignored. This is not only because the number of repetitions is small, but also because the size of the region S is significantly different from the pixel size, so that it is substantially out of the relationship that causes moire. Specifically, as shown in FIG. 16, when a plurality of unit pattern areas S are arranged in a certain direction at a predetermined pitch SP1, SP2, the predetermined pitch SP1, SP2 is along a certain direction. In addition, it is preferably 1/4 or more of the dimensions L1 and L2 of the image forming apparatus, or 50 mm or more in application to a home television receiver. The number of closed regions 42 included in the unit pattern region S is preferably 500 or more.

  However, the modification processing of the seam at the boundary between adjacent unit pattern regions (pattern deformation and modification processing for making the seam inconspicuous), and the shape of the unit pattern region (in FIG. 16, a rectangle is used, but the other 3 (In FIG. 16, the rectangular unit pattern areas S are arranged vertically and horizontally on the grid. However, even if the unit pattern area S is rectangular, If the arrangement pitches SP1 and SP2 of the unit pattern area S are 1/10 or more of the dimensions L1 and L2 of the image forming apparatus, depending on the device such as an arrangement such as brickwork) Alternatively, it has been found that when it is 20 mm or more in application to a home television receiver or a display device for a portable terminal, the striped pattern and the shading unevenness can be made sufficiently inconspicuous.

(Combination with coloring filter)
The optical sheet 30 described above substantially does not cause moiré with the pixel P and does not cause unevenness in density. However, although the detailed cause is currently unknown, when it is installed on the light exit surface 15a of the image forming apparatus 15, a fine flicker (aggregation of minute bright spots) may occur in the image depending on the conditions. In order to make such flickering inconspicuous, in the optical sheet 30, in another sheet-like member included in the image forming apparatus 10, or in an appropriate position in the other image forming apparatus 10, a specific wavelength region in visible light It is effective to provide a colored filter having an absorption spectrum inside. The coloring filter may be an achromatic color (black to gray) or a chromatic color (blue, brown, green, etc.), but an achromatic color that has little influence on the color of the image is preferred.

(Use)
The optical sheet 30 and the image forming apparatus 10 described above can be used for various purposes. In particular, a plasma display (PDP) device used for a display unit of a television receiver, various measuring instruments and instruments, various office equipment, various medical equipment, computer equipment, telephones, electric signboards, various game machines, etc., a cathode ray tube It is suitable for application to an image display device such as a display (CRT) device, a liquid crystal display device (LCD), and an electroluminescent display (EL) device, and particularly suitable for application to a plasma display device. In addition, the optical sheet 30 described above is used to prevent peeping or direct sunlight on the windows of buildings such as houses, schools, hospitals, offices, stores, etc., vehicles, aircraft, ships, etc. It can also be used for applications such as diffusion relaxation.

DESCRIPTION OF SYMBOLS 10 Image display apparatus 10a Display surface 15 Image formation apparatus, Image display panel 15a Light emission surface, Image formation surface 30 Optical sheet 32 Main body part 32a One side 35 Unit lens 40 Array pattern 42 Closed area 44 Line part 46 Branch point 48 Boundary line Minute XA Voronoi region XB Voronoi boundary XP Voronoi point

Claims (6)

An optical sheet used in an overlapping manner with an image forming apparatus,
A sheet-like body,
A plurality of unit lenses arranged on one surface of the main body,
On one surface of the main body, a line portion composed of a boundary line segment extending between two adjacent unit lenses is defined,
Both ends of each boundary line segment of the line part form a branch point connecting to two or more other boundary line segments,
The line portion defines a closed region surrounded by the boundary line segment, and the unit lenses are arranged on the main body portion so that one unit lens is disposed in one closed region. ,
The line portion includes a closed region surrounded by five boundary segments, a closed region surrounded by six boundary segments, and a closed region surrounded by seven boundary segments. Including an area containing at least two types selected from
Five included in the region, the shape or area of the plurality of closed area surrounded by the same number of boundary segments of six or seven are rather constant,
The said line part is an optical sheet containing the area | region where the average of the number of the boundary line segments extended from one branch point is more than 3.0 and less than 4.0 . 2. The optical sheet according to claim 1, wherein the line portion includes a region in which an average number of boundary line segments extending from one branch point is larger than 3.0 and equal to or smaller than 3.1 . The area includes a closed area surrounded by the six boundary lines, optical sheet according to claim 1 or 2. The optical sheet according to any one of claims 1 to 3, wherein the area includes the largest number of closed areas surrounded by six boundary line segments. Of the closed regions included in the region, the number of closed regions surrounded by k boundary segments is N _k .
When k is an integer satisfying 3 ≦ k ≦ 5, N _k ≦ N _{k + 1} is satisfied,
The optical sheet according to any one of claims 1 to 4 , wherein N _k ≥ N _{k + 1} when k is an integer satisfying 6 ≤ k. An image forming apparatus;
Wherein provided on the image forming apparatus, and a optical sheet according to any one of claims 1 to 5, the image display device.

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