Pseudo-random dot pattern and method for creating the same

Abstract

To manufacture a dummy random dot pattern more easily by a geometric method.SOLUTION: The dummy random dot pattern has a dot arrangement in which a first oblique lattice region and a second oblique lattice region are repeatedly arranged with a predetermined space in between in a y-direction, the first oblique lattice region being a region in which a plurality of arrangement axes a1 along which dots are arranged in an x-direction at predetermined pitches in an xy-flat surface are arranged in a b-direction, which obliquely intersects with the x-direction at an angle of α, and the second oblique lattice region being a region in which a plurality of arrangement axes a2 along which dots are arranged in the x-direction at predetermined pitches are arranged in a c-direction, which is reversed with respect to the x-direction.SELECTED DRAWING: Figure 1A

Description

[Technical Field]

[0001] The present invention relates to a pseudo-random dot pattern and a method for creating the same. [Background technology]

[0002] A random dot pattern refers to a state where the arrangement of dots lacks regularity or reproducibility, making it unpredictable. In contrast, a pseudo-random dot pattern appears to be a random dot pattern, but the arrangement of dots does have regularity and reproducibility, making it predictable. Here, "dot" refers to a tiny point or structure.

[0003] Applying a pseudo-random dot pattern to a light diffusion sheet can prevent the generation of diffraction patterns (Patent Documents 1, 2, and 3). In this case, it is required that there is no overlap between the dots, the dot pattern is irregular enough not to produce moiré fringes, and the distribution of the dots is uniform enough not to be visually observable and has a predetermined number density.

[0004] Pseudo-random dot patterns are also used for distance measurement and other applications. For example, a depth camera (Microsoft Kinect®) that uses a projector with microlenses arranged in a pseudo-random dot pattern is well-known.

[0005] One method for creating a pseudo-random dot pattern is to generate the position of each dot using a linear feedback shift register, as described in Patent Document 1. Methods using molecular dynamics have also been proposed (Non-Patent Document 1). [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2010-49267 [Patent Document 2] Special Publication No. 2006-502442 [Patent Document 3] Special Publication No. 2019-510996 [Non-patent literature]

[0007] [Non-Patent Document 1] Information Processing Society of Japan Research Report, Vol.2012-XL, No.8, 2012 / 5 / 14 [Overview of the project] [Problems that the invention aims to solve]

[0008] Conventional methods for creating pseudo-random dot patterns have been approached with the need for a way to create pseudo-random dot patterns with desired number density and periodicity more quickly and easily.

[0009] In contrast, the present invention aims to enable the creation of pseudo-random dot patterns more easily using geometric methods. [Means for solving the problem]

[0010] The inventors of the present invention conceived that a pseudo-random dot pattern can be created by repeatedly arranging, with spacing in the y direction, a first rhombic lattice region having an array axis in the b direction that intersects the x direction at an angle α, and a second rhombic lattice region having an array axis in the c direction, which is the inversion of the b direction with respect to the x direction, in the xy plane. This led to the completion of the present invention.

[0011] In other words, the present invention provides a first orthorhombic lattice region in which, in the xy plane, the array axis a1 of dots arranged at a predetermined pitch in the x direction is arranged in multiple directions b that intersect the x direction at an angle α, The present invention provides a pseudo-random dot pattern in which a dot array axis a2, in which dots are arranged at a predetermined pitch in the x-direction, is repeatedly arranged in a second orthorhombic lattice region in the c-direction, which is the inversion of the b-direction with respect to the x-direction, at predetermined intervals in the y-direction.

[0012] In addition, the present invention provides a method for creating a pseudo-random dot pattern in the xy plane, in which a plurality of first rhombic lattice regions are arranged in a b direction that is obliquely intersecting the x direction at an angle α with an array axis a1 of dots arranged in the x direction at a predetermined pitch, and a plurality of second rhombic lattice regions are arranged in a c direction obtained by reversing the b direction with respect to the x direction, with an array axis a2 of dots arranged in the x direction at a predetermined pitch. The pseudo-random dot pattern is repeatedly arranged at a predetermined interval in the y direction. Note that this method for creating a pseudo-random dot pattern can also be referred to as a method for designing a pseudo-random dot pattern.

[0013] Furthermore, the present invention provides a filler-containing film in which fillers are arranged in a pseudo-random dot pattern in a resin layer in the xy plane, a first rhombic lattice region in which a plurality of array axes a1 of fillers arranged in the x direction at a predetermined pitch are arranged in a b direction that is obliquely intersecting the x direction at an angle α, and a second rhombic lattice region in which a plurality of array axes a2 of fillers arranged in the x direction at a predetermined pitch are arranged in a c direction obtained by reversing the b direction with respect to the x direction, are repeatedly arranged at a predetermined interval in the y direction.

Advantages of the Invention

[0014] ​According to the present invention, a first rhombic lattice region formed by an array axis in the x direction and an array axis in the b direction obliquely intersecting the x direction at an angle α, and an array axis in the x direction and an array axis in the c direction (in other words, an array axis in the c direction obliquely intersecting the x direction at an angle -α) obtained by reversing the b direction with respect to the x direction are repeatedly arranged. Therefore, as a whole dot pattern, the axial direction intersecting the x direction becomes a zigzag pattern. For this reason, the pseudo-random dot pattern of the present invention can be used for various products using a pseudo-random dot pattern. For example, when the pseudo-random dot pattern of the present invention is used for a light diffusing sheet, no moire fringes occur, there is no dot overlap, and a light diffusing sheet in which dot unevenness cannot be recognized by microscopic observation can be obtained. When the pseudo-random dot pattern of the present invention is used for a dot projector, a pseudo-random dot pattern used for distance measurement or the like can be projected onto an object.

[0015] In addition, since the pseudo-random dot pattern of the present invention has a predetermined periodicity, it is possible to easily inspect whether or not the pseudo-random dot pattern is actually formed in a product on which the pseudo-random dot pattern is formed.

Brief Description of Drawings

[0016] [Figure 1A] FIG. 1A is a plan view for explaining dot arrangement in the pseudo-random dot pattern 10A of the embodiment. [Figure 1B] FIG. 1B is a plan view for explaining dot arrangement in the pseudo-random dot pattern 10B of the embodiment. [Figure 1C] FIG. 1C is a plan view for explaining dot arrangement in the pseudo-random dot pattern 10C of the embodiment. [Figure 1D] FIG. 1D is a plan view for explaining dot arrangement in the pseudo-random dot pattern 10D of the embodiment. [Figure 1E] FIG. 1E is a plan view for explaining dot arrangement in the pseudo-random dot pattern 10E of the embodiment. [Figure 1F]Figure 1F is a plan view illustrating the dot arrangement in the pseudo-random dot pattern of the embodiment. [Figure 1G] Figure 1G is a plan view illustrating the dot arrangement in the pseudo-random dot pattern of the embodiment. [Figure 1H] Figure 1H is a plan view illustrating the dot arrangement in the pseudo-random dot pattern of the embodiment. [Figure 1I] Figure 1I is a plan view illustrating the dot arrangement in the pseudo-random dot pattern of the embodiment (non-orthogonal coordinate system). [Figure 1J] Figure 1J is a plan view illustrating the arrangement of fillers in the filler-containing film of the example. [Figure 1K] Figure 1K is a plan view illustrating the filler arrangement in the filler-containing film of the example. [Figure 1L] Figure 1L is a plan view illustrating the filler arrangement in the filler-containing film of the example. [Figure 2A] Figure 2A is a cross-sectional view of filler-containing film 100A, in which the filler has a pseudo-random dot pattern as described in the example. [Figure 2B] Figure 2B is a cross-sectional view of filler-containing film 100B having a pseudo-random dot pattern of the example. [Figure 3] Figure 3 is a cross-sectional view of filler-containing film 100C having a pseudo-random dot pattern of the example. [Figure 4A] Figure 4A is a plan view showing the pseudo-random dot pattern 10A of the embodiment superimposed on a fan-out type region in which rectangular regions are arranged radially. [Figure 4B] Figure 4B is a plan view showing a parallel region formed by arranging rectangular regions in parallel, overlaid with the pseudo-random dot pattern 10A of the embodiment. [Figure 5A] Figure 5A shows the overlap between the individual rectangular regions constituting the fan-out type region and the filler in a simulation in which a filler-containing film with a filler arrangement similar to that of Experimental Example 1 is heat-pressed onto a fan-out type region. [Figure 5B] Figure 5B shows the overlap between the individual rectangular regions constituting the fan-out type region and the filler in a simulation in which a filler-containing film with a filler arrangement similar to that of Experimental Example 3 is heat-pressed onto a fan-out type region. [Figure 5C] Figure 5C shows the overlap between the individual rectangular regions constituting the fan-out type region and the filler in a simulation in which a filler-containing film with a filler arrangement similar to that of Experimental Example 4 is heat-pressed onto a fan-out type region. [Figure 5D] Figure 5D shows the overlap between the individual rectangular regions constituting the fan-out type region and the filler in a simulation in which a filler-containing film with a filler arrangement similar to that of Experimental Example 5 is heat-pressed onto a fan-out type region. [Modes for carrying out the invention]

[0017] An example of the pseudo-random dot pattern of the present invention will be described in detail below with reference to the drawings. In each figure, the same reference numerals represent the same or equivalent components.

[0018] Regarding the evaluation of the randomness of the pseudo-random dot pattern of the present invention, as shown in Figure 4A, two articles having fan-out type regions 21 on their surface, in which rectangular regions 20 are arranged radially, are placed facing each other, and a filler-containing film (a film in which filler 1 is arranged in the pseudo-random dot pattern), which is one embodiment of the use of the pseudo-random dot pattern, is sandwiched between them and pressed or heat-pressed. The focus is on how evenly the rectangular regions 20 and filler 1 overlap within the fan-out type region 21. The fan-out type region is assumed in the evaluation of the randomness of the pseudo-random dot pattern because it contains a region where the rectangular region 20 extends in a direction perpendicular to the short side direction (x direction in the figure) of the rectangular region 20 (y direction in the figure), and a region that is inclined at a different angle to that direction, making it suitable for evaluating randomness. In a filler-containing film, if the filler 1 is arranged completely randomly and uniformly, the rectangular regions 20 and the filler 1 will overlap uniformly within the fan-out region 21. However, if the filler is arranged in a grid pattern on the film, such as a square grid or a hexagonal grid, then even if many fillers overlap in one rectangular region 20 within the fan-out region 21, there will be almost no overlap with the filler in other rectangular regions 20.

[0019] As a contrast, instead of the fan-out type region 21, we consider the case where an article having a parallel type region 22 in which rectangular regions 20 are arranged in parallel, as shown in Figure 4B, is pressed or heat-pressed with a filler-containing film, and similarly we focus on how evenly the rectangular regions 20 and the filler 1 overlap within the parallel type region 22.

[0020] <Dot Pattern> Figure 1A is a plan view illustrating the dot arrangement in a pseudo-random dot pattern 10A of one embodiment. This dot arrangement consists of a first rhombic lattice region 11 and a second rhombic lattice region 12 alternately arranged in the y direction in the xy plane. Here, the first rhombic lattice region 11 is a region where multiple array axes a1, in which dots 1 are arranged at a constant pitch pa in the x direction, are arranged obliquely in the b direction at an angle α with respect to the x direction. The second rhombic lattice region 12 is a region where multiple array axes a2, in which dots 1 are arranged at the aforementioned pitch pa in the x direction, are arranged in the c direction. This c direction is the direction obtained by reversing the b direction with respect to a line parallel to the x direction as the axis of symmetry. Alternatively, the c direction is the direction obliquely intersecting the x direction at an angle -α. Therefore, this dot arrangement can also be seen as being based on a curved array d enclosed by a dashed line in Figure 1A, which consists of the arrangement in the b direction of the first rhombic lattice region 11 and the arrangement in the c direction of the second rhombic lattice region 12.

[0021] The dot pitch on the array axis a2 of the second rhombic lattice region 12 may be different from the dot pitch pa on the array axis a1 of the first rhombic lattice region 11. However, for design convenience in dot arrangement, it is preferable to make the pitches pa of array axis a2 and array axis a1 equal. Furthermore, the dot pitch pa on the array axis a1 of the first rhombic lattice region 11 itself only needs to have regularity and does not necessarily need to be constant. For example, two different pitches may appear at a predetermined period. The same applies to the dot pitch on the array axis a2 of the second rhombic lattice region 12.

[0022] As in this embodiment, with respect to the arrangement of the dots 1, if a first rhombic grid region 11 with the x-direction and the b-direction oblique to the x-direction as the array axes, and a second rhombic grid region 12 with the x-direction and the c-direction (the inverse of the b-direction) as the array axes are alternately repeated, then, as shown in Figure 4A, the degree of overlap between the fan-out type region 21, in which the rectangular regions 20 are arranged radially, and the dot pattern, as shown in Figure 4B, the degree of overlap between each rectangular region 20 and the dots becomes uniform, allowing us to confirm the irregularity and uniformity of the dot pattern. In contrast, if the dots in the dot pattern are arranged only in the first rhombic grid region 11 or only in the second rhombic grid region 12, the number of dots overlapping with each rectangular region 20 and the variation in the distribution of dots within each rectangular region 20 will increase. In any of the rectangular regions 20 within the fan-out type region 21, the direction of the arrangement axis of the dots 1 arranged in the rhombic grid will coincide with the longitudinal direction of the rectangular region 20, causing a sharp decrease in the degree of overlap of the dots 1 arranged at the edges of the rectangular region 20, or forming densely packed areas within any of the rectangular regions 20 where multiple dots are close together. The pseudo-random dot pattern of the present invention has excellent randomness, so such non-uniformity is less likely to occur.

[0023] As will be described later, one example of the use of the pseudo-random dot pattern of the present invention is a filler-containing film in which a filler that provides functionalities such as light diffusion, conductivity, heat dissipation, and electromagnetic shielding is arranged in a resin layer using the pseudo-random dot pattern of the present invention. Figures 4A and 4B show an example of heat-pressing a filler-containing film between two articles having a fan-out type region 21 or a parallel type region 22. When heat-pressing these articles together, it is preferable to align the x-direction, which is the direction of the array axis a1 or array axis a2 of the filler (dots) 1, with the same direction as the array direction of the rectangular region 20, so that the number of dots overlapping the rectangular region is equal in the rectangular region on the left side of the page and the rectangular region on the right side of the page. From the viewpoint of convenience in using the filler-containing film, it is preferable to align the direction of the array axis a1 or array axis a2 with the longitudinal direction of the filler-containing film. Alternatively, it is preferable to align the short-side direction (x-direction) of the rectangular region 20 with the longitudinal direction of the filler-containing film. Furthermore, it is preferable that the number of repetitions of the first orthorhombic lattice region 11 and the second orthorhombic lattice region 12 of the filler-containing film is sufficient with respect to the length of the rectangular region 20 in the longitudinal direction (y direction). For example, this number of repetitions is preferably 1 or more times the length of the rectangular region 20, and more preferably 3 or more times. In other words, it is preferable that the repeating pitch in the y direction of the first orthorhombic lattice region 11 and the second orthorhombic lattice region 12 of the filler-containing film is less than or equal to the length of the rectangular region 20, and more preferably 1 / 3 or less. Alternatively, it is preferable to determine the number of bends in the array axis formed by the array axis in the b direction of the first orthorhombic lattice region 11 and the array axis in the c direction of the second orthorhombic lattice region 12 so that the number of fillers overlapping each rectangular region 20 is greater than or equal to a predetermined number or within a predetermined range. The number of fillers is determined according to the application and usage, and may be set to, for example, 3 or more, more preferably 11 or more. Of course, it is not limited to this.

[0024] Furthermore, in the first orthorhombic lattice region 11, with respect to the angle α between the x-direction and b-direction of the array axis a1, when the filler-containing film is heat-pressed to the fan-out type region 21, the absolute value of angle α is made smaller than the minimum absolute value of the fan-out angle β. As a result, in any of the rectangular regions 20 constituting the fan-out type region 21, the longitudinal direction of the rectangular region 20 and the b-direction no longer coincide in the first orthorhombic lattice region 11. This prevents a sharp decrease in the degree of overlap between the filler present at the longitudinal edge of the rectangular region 20 and the rectangular region, and prevents a large number of fillers from being connected on the rectangular region 20. On the other hand, when the region to be heat-pressed with the filler-containing film is a parallel region 22 (Figure 4B) in which rectangular regions 20 whose longitudinal direction is perpendicular to the x-direction are arranged in parallel in the x-direction, or a parallel region (not shown) in which rectangular regions whose longitudinal direction is oblique to the x-direction are arranged in parallel in the x-direction, it is preferable to set the absolute value of angle α to be less than or equal to the absolute value of angle β formed by the arrangement direction of the rectangular regions 20 and the longitudinal direction of the rectangular regions 20, because when the arrangement direction of the rectangular regions 20 and the longitudinal direction of the rectangular regions 20 are perpendicular, the number of fillers overlapping with the rectangular regions is stable. Furthermore, it is also preferable when regions with an arrangement direction of the rectangular regions 20 extending in the x-direction and regions extending in the y-direction are mixed, because the number of fillers overlapping with these regions is stable.

[0025] Furthermore, in the second rhombic lattice region 12, the c direction is the direction obtained by inverting the b direction with respect to the x direction, and the angle between the x direction and the c direction is -α. By setting the angle α as described above, the longitudinal direction of the rectangular region 20 and the c direction no longer coincide in the second rhombic lattice region 12, so the same effect as described above can be obtained.

[0026] If the angle α is 90°, the filler arrangement in the first orthorhombic lattice region 11 and the second orthorhombic lattice region 12 will be a square lattice or a rectangular lattice, so the angle α may also be expressed as the strain s in the x-direction of the square lattice or rectangular lattice (Figure 1A). If the strain s is greater than the average diameter of the filler, the fillers within the same orthorhombic lattice region will be less likely to connect in the y-direction on a single rectangular region when the filler-containing film and the rectangular region 20 are heat-pressed together. On the other hand, if the strain s is less than or equal to the average diameter of the filler, preferably less than the average diameter, the fillers of the filler-containing film and the rectangular region 20 will be more likely to overlap, even if the width of the rectangular region 20 is narrow.

[0027] Furthermore, the angle that direction c makes with the x direction does not have to be exactly the same as the angle α with the sign reversed. That is, the absolute value of the angle that direction b makes with the x direction and the absolute value of the angle that direction c makes with the x direction do not have to be exactly the same, and may differ for each rhombic lattice region. In this case, it is preferable that the sum of these angles in all rhombic lattice regions is 0°.

[0028] By the way, if we let P1 and P2 be the center positions of adjacent dots on an arbitrary array axis a11, and let P3 be the center position of a dot on an array axis a1(a12) adjacent to array axis a11 whose x-direction position is between P1 and P2, then if ∠P3P1P2≠∠P3P2P1, then as shown in Figure 1A, the dot arrangement of the first rhombic lattice region 11 and the dot arrangement of the second rhombic lattice region 12 are symmetrical and different, and even if these regions are translated, the dot arrangements will not overlap. In other words, the extension of an arbitrary array axis that intersects the x-direction obliquely in one of these rhombic lattice regions 11 and 12 will not also be an array axis in the other region.

[0029] In contrast, as shown in Figure 1B, if ∠P3P1P2 = ∠P3P2P1, then the dot arrangement of the first rhombic lattice region 11 and the dot arrangement of the second rhombic lattice region 12 are themselves equal. Here, The distance between the first rhombic lattice region 11 and the second rhombic lattice region 12 is L3. In the first orthorhombic lattice region 11, the distance between adjacent array axes a1 is L1. In the second orthorhombic lattice region 12, the distance between adjacent array axes a2 is L2. Ld is the x-direction displacement between the nearest dots in the adjacent array axis a1 of the first rhombic lattice region 11 and the array axis a2 of the second rhombic lattice region 12. The pitch of array axes a1 and a2 is pa In that case, If L3 = L1, L2 and Ld = (1 / 2) × pa, then the same array axis in the b direction as the array axis in the first rhombic lattice region 11 also exists in the second rhombic lattice region 12, and the extension of the array axis in the second rhombic lattice region becomes the array axis in the b direction of the first rhombic lattice region. In this way, with respect to the array axis that intersects the x direction, if the array axis of one of the two rhombic lattice regions 11 and 12 becomes the array axis of the other rhombic lattice region, then the array axis intersecting the x direction in the entire dot pattern will not be zigzag, and such a dot arrangement will not achieve the effects of the present invention. Therefore, such a dot arrangement is excluded from the present invention.

[0030] On the other hand, if ∠P3P1P2≠∠P3P2P1, then L3=L1,L2 and Ld=(1 / 2)×pa, the effects of the present invention can be obtained. For example, if the average diameter of the filler is 3.2 μm, and the number of array axes in the x-direction in the first orthorhombic lattice region 11 and the second orthorhombic lattice region 12 is 2 each, then L1=L2=L3=9.5 μm, pa=9 μm, Ld=(1 / 2)×pa=4.5 μm, strain amount s=2.25 μm, α=76°, and number density 12000 particles / mm 2 This can be done (Figure 1J).

[0031] Furthermore, using a filler with a similar average diameter, and setting the number of x-axis arrangements in the first orthorhombic lattice region 11 and the second orthorhombic lattice region 12 to 2, the values ​​were L1=L2=10.4μm, L3=8.8μm, pa=8.8μm, Ld=(1 / 2)×pa=4.4μm, strain s=2.2μm, α=78°, and number density 12000 particles / mm². 2 This can be done (Figure 1K).

[0032] Using fillers with similar average diameters, and setting the number of x-axis arrangements in the first orthorhombic lattice region 11 and the second orthorhombic lattice region 12 to 2, the parameters are L1=L2=L3=7.5μm, pa=8.4μm, Ld=(1 / 2)×pa=4.2μm, strain s=2.1μm, α=75°, and number density 16000 particles / mm². 2 This is also possible (Figure 1L). In this way, the pitch pa may be greater than L1, L2, and L3.

[0033] In the embodiments shown in Figures 1J, 1K, and 1L, the displacement Ld is defined as half of the pitch pa, and the strain s is defined as half of the displacement Ld. This relationship between pitch pa, displacement Ld, and strain s is preferable for the convenience of designing the pseudo-random dot pattern arrangement of the present invention. Furthermore, it becomes easier to check the arrangement of the dots after applying this dot pattern to any object such as film, resin plate, glass, or metal. For example, by drawing auxiliary lines connecting the center point and outer tangents of the filler in an image of a filler-containing film, the displacement Ld and strain s can be easily checked.

[0034] Furthermore, as shown in Figure 1B, even if ∠P3P1P2=∠P3P2P1, if L3≠L1,L2, or Ld≠(1 / 2)×pa, the first rhombic lattice region 11 and the second rhombic lattice region 12 can be identified as separate regions. In the overall dot pattern, the array axes intersecting the x-direction become zigzag, and the effects of the present invention can be obtained.

[0035] In this invention, the displacement amount Ld is determined by appropriately widening the distance between dots in the y-direction in the dot pattern and applying a predetermined number density (dots / mm²) to the dot distribution. 2It is preferable that the displacement amount Ld is not zero in order to have both irregularity and uniformity while ensuring the same properties. That is, if the displacement amount Ld is zero, the dots of the first rhombic lattice region and the dots of the second rhombic lattice region that are adjacent in the y direction will overlap in the y direction. For example, when a filler-containing film is constructed with this dot pattern and the filler-containing film is heat-pressed onto a predetermined object, the distance between fillers becomes excessively short in the portion where the fillers of the first rhombic lattice region and the fillers of the second rhombic lattice region overlap in the y direction, making it easy for the fillers to connect with each other. Therefore, it is preferable that the absolute value of the displacement amount Ld is greater than zero, more preferably 0.5 times or more the average diameter of the dots, even more preferably 1 time or more the average diameter of the dots, and particularly preferable to be greater than 1 time the average diameter. On the other hand, the upper limit of the displacement amount Ld is preferably 0.5 times or less the pitch pa of the array axes a1 and a2, more preferably less than 0.5 times, and even more preferably 0.3 times or less.

[0036] The dot arrangement shown in Figure 1C is the same as the dot arrangement shown in Figure 1A, but with the displacement Ld set to 0. When a filler-containing film is constructed with this dot pattern and the filler-containing film is heat-pressed onto an object, the displacement Ld may be set to 0 if the distance L3 is long relative to the amount of filler movement during heat pressing.

[0037] The dot arrangement shown in Figure 1D is obtained by adjusting the displacement amount Ld in the dot arrangement shown in Figure 1A, so that the arrangement axis in the b direction of the first orthorhombic lattice region 11 and the arrangement axis in the c direction of the second orthorhombic lattice region 12 intersect on dot 1. As a result, the axis of symmetry for the reversal in the b and c directions lies on the a1 axis or a2 axis, and the reversed shape is repeated without gaps in the y direction, which is preferable because it simplifies the design of the dot arrangement and the inspection process after arrangement.

[0038] The dot arrangement shown in Figure 1E is obtained by making the distance L3 between the first rhombic lattice region 11 and the second rhombic lattice region 12 different from the distance L1 between adjacent array axes a1 in the first rhombic lattice region 11, or the distance L2 between adjacent array axes a2 in the second rhombic lattice region 12. Regarding these distances L1, L2, and L3, in the present invention, it is preferable to set L1=L2 or L1=L2=L3 from the viewpoint of convenience in designing the dot arrangement and ease of comparing dot densities in a predetermined region. However, if necessary, L3≠L1,L2 or L1≠L2 may also be set.

[0039] Furthermore, the distances L1 and L2 are preferably determined by the layout of the area to be heat-sealed, and there are no particular upper or lower limits on them. For example, if the distances L1 and L2 are small, the filler is more likely to overlap with the area to be heat-sealed, but this also makes it easier for the fillers to connect with each other, so it is preferable that the distances L1 and L2 be 1.4 times or more the average diameter of the filler.

[0040] The pitch pa of the fillers in the array axis a1 of the first orthorhombic lattice region 11 and the array axis a2 of the second orthorhombic lattice region 12 is preferably determined by the layout of the area to be heat-compressed, and there are no particular upper or lower limits. For example, if the pitch pa is too small, the fillers tend to connect with each other, so it is preferable to have a pitch of 1.5 times or more the average diameter of the fillers, and in particular, it can be set to a distance of twice the average diameter plus 0.5 μm or more.

[0041] On the other hand, increasing the pitch pa can reduce the number of fillers required in the filler-containing film. Also, even if the width of the heat-sealing area is narrow, if the length of the heat-sealing area is sufficiently long, the number of fillers overlapping the heat-sealing area will satisfy the predetermined number. Therefore, when the arrangement direction of the heat-sealing areas and the x-direction are the same, it is preferable to set the pitch pa to 1 / 2 to 2 / 3 of the minimum width of the effective connection area after the heat-sealing areas are connected via the filler-containing film.

[0042] Furthermore, it is preferable to make the distances L1, L2, and L3 equal to the pitch pa, that is, to make the dot arrangement of the first rhombic lattice region 11 and the second rhombic lattice region 12 a rhombic lattice obtained by distorting a square lattice in the x direction, and to make the distance L3 between the first rhombic lattice region 11 and the second rhombic lattice region 12 equal to the lattice pitch, in order to ensure that the distribution of dots is uniform across the entire surface.

[0043] The dot arrangement shown in Figure 1F is the same as the dot arrangement shown in Figure 1A, but with the number of arrangements n1 for the array axis a1 in the first rhombic lattice region 11 and the number of arrangements n2 for the array axis a2 in the second rhombic lattice region 12 set to 2. Figures 1J, 1K, and 1L, mentioned above, are further detailed embodiments of this arrangement. In the present invention, it is preferable to make the number of arrangements n1 for the array axis a1 in the first rhombic lattice region 11 and the number of arrangements n2 for the array axis a2 in the second rhombic lattice region 12 equal, but they may be different. Furthermore, when constructing a filler-containing film with the pseudo-random dot pattern of the present invention and heat-pressing the filler-containing film onto an article, these number of arrangements n1 and n2 can be determined according to the layout of the area to be heat-pressed, so there are no particular limitations. When the arrangement of the heat-sealed region is fine-pitch, the number of arrangements n1 and n2 is preferably 10 or less, more preferably 4 or less, even more preferably 3 or less, and particularly preferably 2, in order to ensure that the filler overlaps the heat-sealed region and to prevent the fillers from connecting with each other. This is because setting the number of arrangements n1 of the arrangement axis a1 in the first orthorhombic lattice region and the number of arrangements n2 of the arrangement axis a2 in the second orthorhombic lattice region to 2 to 4 results in a finer zigzag pitch of the arrangement axes compared to cases where the number is greater. This allows for a more uniform distribution of the filler in the right and left regions of the fan-out type region when the filler-containing film is heat-sealed to the fan-out type region, and also suppresses contact between the fillers. Although heat-sealing has been described here, it can be inferred that depending on the application, the function can be achieved by forming many rows of minute dots, so the limit on the number of arrangements should be determined according to the purpose.

[0044] The dot arrangement shown in Figure 1G is the same as the dot arrangement shown in Figure 1A, but instead of having a single pitch pa for the dots in the x-direction in the first rhombic lattice region 11, different pitches pa1 and pa2 are alternately repeated. Similarly, in the second rhombic lattice region 12, the dots in the x-direction also alternately have pitches pa1 and pa2. Thus, in this invention, the pitch of the dots arranged in the x-direction only needs to be regular and does not necessarily have to be a constant pitch.

[0045] The dot arrangement shown in Figure 1H is the same as the dot arrangement shown in Figure 1A, but with two first rhombic lattice regions 11a and 11b within the first rhombic lattice region 11, where the arrangement axis in the b direction is shifted in the x direction, and two second rhombic lattice regions 12a and 12b within the second rhombic lattice region 12, where the arrangement axis in the c direction is shifted in the x direction. In this case, the amount of x-direction shift Ld1 between the arrangement axes a1 of two adjacent first rhombic lattice regions 11a and 11b and the amount of x-direction shift Ld2 between the arrangement axes a2 of two adjacent second rhombic lattice regions 12a and 12b may be the same or different.

[0046] Thus, in this invention, it is sufficient that the first rhombic lattice region and the second rhombic lattice region are repeated in the y direction, and they do not necessarily have to be repeated alternately. Furthermore, the x-direction positions of the dot patterns in the first rhombic lattice region that are repeated in the y direction, and the x-direction positions of the dot patterns in the second rhombic lattice region, may be the same or different. On the other hand, it is preferable that the total number of repetitions in the y direction of the array axis a1 of the first rhombic lattice region and the total number of repetitions in the y direction of the array axis a2 of the second rhombic lattice region are equal for a unit length in the y direction.

[0047] In this invention, the x and y coordinates are not limited to orthogonal coordinates. For example, Figure 1I shows the dot arrangement shown in Figure 1H above, but in non-orthogonal coordinates where the x and y directions are not orthogonal. For design convenience, it is preferable to use orthogonal coordinates.

[0048] <Dot structure> In this invention, the dots arranged in the pseudo-random dot pattern refer to minute points or structures, and these minute points may include minute solids such as various fillers. The structure does not refer only to convex or raised areas, but may also be shapes such as concave or recessed areas. The composition of the dots can be appropriately determined according to the object on which the pseudo-random dot pattern is provided. For example, in a moth-eye film, the dots can be nanostructures formed as concave or convex areas on a transparent resin substrate, and in an embossed film, they can be concave or convex areas on the order of microns. In a light-diffusing sheet, the dots can be light-diffusing fillers, in sheets with electrical functionality, sheets with electromagnetic shielding properties, etc., they can be conductive fillers, and in a heat-dissipating sheet, the thermal conductivity of the dots is adjusted according to the substrate holding the dots. In this case, the thermal conductivity may be different, and the surface area may be increased. In a dot projector, the dots can be microlenses.

[0049] The shape of the dot may be the shape of the filler itself, or the shape onto which the filler has been transferred. The shape of the dot may be spherical or a similar raised shape (a rounded shape), rod-shaped, or highly flexible. The tip may be pointed or rounded. It may also be a complex shape with a spherical shape and even smaller attached particles. Furthermore, the aspect ratio (length in the xy plane relative to height and depth) may be adjusted as appropriate according to the function, and there are no particular restrictions.

[0050] Specific examples of the dot configuration itself can be the same as those described in Japanese Patent Publication No. 2018-124595, Japanese Patent Publication No. 2016-29446, Japanese Patent Publication No. 2015-132689, WO2016 / 068166, WO2016 / 068171, WO2018 / 074318, WO2018 / 101105, WO2018 / 051799, etc.

[0051] <Dot size and number density> In this invention, the size of dot 1 and the number density (dots / mm²) in the xy plane are defined. 2) can be appropriately set according to the object to which the pseudo-random dot pattern is provided, and the size can usually be less than 1000 μm in diameter, for example, several tens of nm to several hundreds of μm, particularly 200 μm or less from the visible light wavelength. The number density can usually be 10 particles / mm 2 or more, or 30 particles / mm 2 or more, and the upper limit can be 10 9 particles / mm 2 or less, or 10 7 particles / mm 2 or less, or 10 5 particles / mm 2 or less, or within the range of 70000 particles / mm 2 or less. Also, the size of dot 1 may be smaller than several tens of nm. Particularly when the dot is a filler, from the viewpoint of workability during manufacturing, it is desirable that the upper limit of the filler diameter is 200 μm or less, preferably 50 μm or less, more preferably 30 μm or less. Also, from the viewpoint of inspection during manufacturing, it is desirable that the lower limit of the filler diameter is 0.5 μm or more, preferably 0.8 μm or more, still more preferably 1 μm or more.

[0052] For example, when arranging nanostructures in a pseudo-random dot pattern on a transparent substrate to form an optical structure such as a moth-eye film or a structure by unevenness, the number density of the nanostructures can be (10 - 1000)×10 6 particles / mm 2 .

[0053] In the present invention, the filler may have an optical function (functions possessed by optical elements such as light intensity adjustment, optical filters, light diffusibility, light shielding properties, light wavelength conversion, absorption ability of a specific wavelength possessed by pigments, etc.), may have insulating properties, conductivity, heat conductivity, etc., or may have properties used for surface treatment such as hydrophilicity or lipophilicity. When obtaining a functional film (or a surface having functionality) having various optical properties, electromagnetic shielding properties, conductivity, heat dissipation properties, surface modification, etc. by arranging such a filler in a pseudo-random dot pattern in a resin layer, the number density of the filler is 500000 particles / mm 2 or less, 350000 particles / mm 2Below, 10~100000 pieces / mm 2 , or 30-70,000 pieces / mm 2 This can be achieved. More specifically, for example, when constructing a light-diffusing sheet by arranging light-diffusing fillers in a pseudo-random dot pattern on a resin layer, the number density of light-diffusing fillers with a diameter of 1 μm or more can be 100 to 500,000 pieces / mm². 2 This can be done, preferably at a density of 10 to 100,000 pieces / mm 2 It can be done this way.

[0054] The number density of dots can be determined using a metallurgical microscope, electron microscope (e.g., SEM or TEM), etc., depending on the size of the dots. Alternatively, the number density may be measured using a three-dimensional surface measurement device, or it may be determined by measuring observed images using image analysis software (e.g., WinROOF (Mitani Corporation) or A-Image-kun (registered trademark) (Asahi Kasei Engineering Corporation)).

[0055] In this invention, the number density of dots is equal to the number density when the angle α is 90° and the first rhombic lattice region 11 and the second rhombic lattice region 12 are square or rectangular lattices instead of rhombic lattices. Therefore, the pitch pa and distances L1 and L2 can be determined by calculating the inter-lattice distance using such a square or rectangular lattice.

[0056] <Applications of pseudo-random dot patterns> The pseudo-random dot pattern of the present invention may be used not only in various applications where a pseudo-random dot pattern has been conventionally provided, but also in applications where a pseudo-random dot pattern was not necessarily required. For example, the pseudo-random dot pattern of the present invention can be used in moth-eye films, dot projectors, light-diffusing sheets, etc., and can also be used in functional films having various functions such as light wavelength conversion, conductivity, heat dissipation, and electromagnetic shielding. It may also be used in household goods and their materials that utilize its surface properties. The manufacturing methods themselves can be the same as conventional methods. Furthermore, when providing a pseudo-random dot pattern to a predetermined object, it is not necessarily required to provide it to the entire surface of the object; for example, the pseudo-random dot pattern may be scattered like a sea-island structure.

[0057] Pseudo-random dot patterns are a form of regular arrangement, but they can also be used in applications that are intermediate between those where random patterns are used and those where dots are regularly arranged in a grid shape such as rectangles or regular polygons. This includes methods for verifying the effects of random and regular arrangements in detail. For example, in nanostructures, wettability is sometimes controlled by controlling the aspect ratio and repeating pitch of the structure and the contact angle derived from the material, but it is expected that the direction of wettability can be controlled by using a pseudo-random dot pattern. In applications where properties depend on the surface shape on the nano to micrometer order (electrode materials, permeable membranes, etc.), life sciences, medical and bio applications (cell disruption, cell culture, etc.), improved functionality and the emergence of new functions can be expected by using pseudo-random dot patterns. Furthermore, the indentations and convex shapes arranged in the pseudo-random dot pattern can also be used as molds. In various applications of pseudo-random dot patterns, there may be other layers in addition to the layer with the pseudo-random dot pattern. For example, a film body with a pseudo-random dot pattern made of filler, or a layer with a pseudo-random dot pattern as an uneven structure on the film surface, may be attached to another article via an adhesive or bonding agent. Another layer may be interposed between the film body with the pseudo-random dot pattern and the other article. The manufacturing methods for these can be referenced from the previously mentioned publications.

[0058] Thus, the pseudo-random dot pattern can be developed in various ways depending on the substrate on which it is applied. The present invention also includes the application of the pseudo-random dot pattern of the present invention for various purposes.

[0059] <Method for manufacturing pseudo-random dot patterns> The method for manufacturing the pseudo-random tot pattern itself can be one of known methods. For example, moth-eye film and similar materials can be manufactured as described in WO2012 / 133943. When using fillers, they can be manufactured as described in WO2016 / 068166, WO2016 / 068171, WO2018 / 074318, WO2018 / 101105, and WO2018 / 051799.

[0060] Furthermore, as a method for manufacturing various sheets using minute solids such as light-diffusing fillers, insulating or conductive fillers, a resin layer of the target sheet is formed on a release substrate with a smooth surface, such as a PET film. Meanwhile, a mold is created in which the recesses are formed in a pseudo-random dot pattern. Resin is poured into this mold to create a resin mold, the minute solids are filled into the recesses of this resin mold, the aforementioned resin layer is placed over them, the minute solids are transferred to this resin layer, the minute solids are pressed into the resin layer, and if necessary, further resin layers are laminated to obtain a sheet in which the minute solids are arranged in a pseudo-random dot pattern when viewed from above. The sheet with minute solids provided in the resin layer can also be used to perform a process of providing minute solids to the surface of a separate object. More specific methods for manufacturing the filler-containing film itself can be found in publications such as WO2016 / 068171, WO2018 / 74318, WO2018 / 101105, and WO2018 / 051799.

[0061] This allows for the creation of a filler-containing film 100A with a layer configuration in which, for example, as shown in Figure 2A, a single layer of filler (micro-solids) 1 is arranged in a pseudo-random dot pattern on or near the surface of an insulating resin layer 2, and a low-viscosity resin layer 3 is laminated on top of it. Alternatively, as shown in Figure 2B, a filler-containing film 100B may be obtained with a layer configuration in which the low-viscosity resin layer 3 is omitted. On the other hand, as shown in Figure 3, a filler-containing film 100C may be obtained in which the filler (micro-solids) 1 is held in the through-holes 2h of an insulating film 2, which are formed in a pseudo-random dot pattern, and low-viscosity resin layers 3A and 3B are laminated on the upper and lower surfaces. In this case, the insulating film 2 is made of a resin layer that is less susceptible to deformation due to heating and pressurizing than the low-viscosity resin layers 3A and 3B. The relationship between the physical properties of the laminated resin layers is not limited to these and can be appropriately changed depending on the purpose.

[0062] Furthermore, there are no particular limitations on the smoothness of the surface on which the pseudo-random dot pattern of the present invention is applied. It may be smooth, have irregularities, or have undulations.

[0063] A pseudo-random dot pattern may be applied to a smooth surface to create a wavy texture, or a pseudo-random dot pattern may be applied to a plane that already has a wavy texture. The wavy texture only needs to be such that the pseudo-random dot pattern can be identified; for example, there may be wavy textures within one period in the y-direction of Figure 1A, or multiple periods may be contained within a single wavy texture.

[0064] The material of the surface on which the pseudo-random dot pattern is provided is not particularly limited and may be a known resin, or an inorganic material such as metal, alloy, glass, or ceramic. It may also be an organic-inorganic hybrid or a surface in which organic and inorganic materials are mixed (for example, a transparent conductive film on which ITO wiring is provided). As a method for providing the pseudo-random dot pattern on a flat resin film, the method described in the previously cited publication can be used. [Examples]

[0065] The present invention will be described in detail below with reference to examples. A simulation was conducted assuming that a filler-containing film, in which fillers are arranged in a pseudo-random dot pattern on a resin film, is sandwiched between fan-out type regions arranged radially and heat-pressed. In this case, considering that the fillers move due to the resin flow of the resin film, the following evaluation was made regarding whether or not the fillers are retained in the fan-out type regions.

[0066] Experimental Examples 1-5 Table 1 shows the specifications for fan-out type region A or B. Table 2 shows the filler arrangement (spherical filler diameter 3 μm) and the evaluation items (a) to (d) and evaluation results when the filler-containing film is heat-pressed for experimental examples 1 to 5. Of these, experimental examples 1 to 3 are embodiments of the present invention. Note that the following evaluation criteria are convenient criteria for evaluating pseudo-randomness.

[0067] In relation to the evaluation results of (d), the number density was 16,000 particles / mm³ for the filler arrangements in experimental examples 1, 3, 4, and 5. 2 The simulation results for the number of fillers overlapping the rectangular region of region B in this case (the expansion ratio of the distance between fillers in the rectangular region and the gap region between the two rectangular regions is the same as in Table 1) are shown in Figures 5A to 5D.

[0068] In this simulation, the arrangement direction of each rectangular region and the x-direction of the filler-containing film (Figures 1A and 1F) were set to be the same direction. Furthermore, the expansion ratio of the distance between fillers on the rectangular region in the x-direction or y-direction, and the expansion ratio of the distance between fillers in the gap region between two rectangular regions in the x-direction or y-direction, as shown in Table 1, are average values ​​obtained by measuring the corresponding ratio of the filler-containing film multiple times in similar regions beforehand.

[0069] (a) Minimum number of overlaps between individual rectangular regions and fillers (simulation in fan-out region A) OK: 5 or more NG: 4 or less (b) Number of fillers connected in the longitudinal direction of the rectangular regions in the gap region between the two rectangular regions (simulation in fan-out type region B) OK: 3 or less NG: 4 or more (c) Number of fillers arranged linearly on the rectangular region (simulation in fan-out region B) OK: 3 or less NG: 4 or more (d) Uniformity of the number of fillers on the left and right sides of the rectangular region that overlaps with the center of the fan-out region in the width direction, at a symmetrical distance from the center (simulation in fan-out region B) Uniform: When the distribution patterns of fillers overlapping rectangular regions that are symmetrically located from the center of the fan-out region in the width direction appear identical. Non-uniform: When the distribution patterns of fillers overlapping with rectangular regions at symmetrical distances from the center of the fan-out region in the width direction do not appear identical.

[0070] [Table 1]

[0071] [Table 2]

[0072] Table 2 shows that experimental examples 1-3 all performed well in terms of evaluation items. In the fan-out type region, the fillers overlapped evenly with each rectangular region, the number of fillers connecting in the y-direction in the gap region and the number of fillers lined up on the rectangular region were reduced, and the overlap between the left and right rectangular regions and the fillers within the fan-out type region was uniform.

[0073] In contrast, in Experimental Example 4, the number of fillers arranged on the rectangular region and the number of fillers connected in the y-direction in the gap region are large, and the left-right uniformity is also poor. Furthermore, in Experimental Example 5, the left-right uniformity is good, but it can be seen that there are not enough fillers overlapping with the rectangular region. Thus, as can be seen from Figures 5A to 5D, the filler arrangement in the experimental examples corresponding to the embodiments of the present invention results in good uniformity of overlap between the fan-out type region and the fillers.

[0074] Experimental Examples 1-5 illustrate the effect of a pseudo-random dot pattern when resin flow affects filler placement; however, the effect of a pseudo-random dot pattern can be obtained without being limited to the presence of fillers in the resin. Furthermore, the use of filler-containing films in which the fillers are arranged in a random dot pattern is not limited to pressing them onto an object. [Explanation of symbols]

[0075] 1. Dot, filler, micro solid 2. Insulating resin layer, insulating film 2h through hole 3, 3A, 3B Low viscosity resin layer 10A, 10B, 10C, 10D, 10E Pseudo-random dot patterns 11, 11a, 11b 1st orthorhombic lattice area 12, 12a, 12b 2nd orthorhombic lattice area 20 rectangular area 21 Fan-out type domain 22 Parallel region 100A, 100B, 100C filler-containing films a1 Array axis of the first orthorhombic lattice region a2 Array axis of the second orthorhombic lattice region b. Direction of the array axis that intersects the array axis x obliquely in the first orthorhombic lattice region. c. Direction of the array axis that intersects the array axis x obliquely in the second orthorectal lattice region. Ld displacement s Strain amount x Rectangular region arrangement direction The direction perpendicular to the yx direction, the direction of the y axis in the xy-plane. Dot pitch on the array axis α is the angle between the x-direction and the b-direction. β is the fan-out angle in the case of a fan-out array, and the angle between the array direction of the rectangular region and the longitudinal direction of the rectangular region in the case of a non-fan-out array. γ The tilt angle of the array axis of the hexagonal lattice with respect to the x-direction.

Claims

1. A film body in which dots are arranged in a pseudo-random dot pattern in the xy plane, In the pseudo-random dot pattern described above, a first rhombic lattice region is formed in which multiple dot array axes a1, where dots are arranged at a predetermined pitch in the x-direction, are arranged obliquely in the b-direction at an angle α (excluding 90°) to the x-direction, and a second rhombic lattice region is formed in which multiple dot array axes a2, where dots are arranged at a predetermined pitch in the x-direction, are arranged in the c-direction, which is the inverse of the b-direction with respect to the x-direction. These regions are repeatedly arranged at predetermined intervals in the y-direction, without the extension of the array axes in the b-direction of the first rhombic lattice region becoming the array axes of the second rhombic lattice region. In the array axis a1 of the adjacent first rhombic lattice region and the array axis a2 of the second rhombic lattice region, the positions of the nearest dots are shifted in the x-direction. A dot is a tiny point or structure arranged in a pseudo-random dot pattern. The aforementioned structure is convex, raised, concave, recessed, or concave-convex, The aforementioned minute dots are fillers arranged in a resin layer, forming a film body.

2. The film body according to claim 1, wherein a first rhombic lattice region and a second rhombic lattice region are alternately and repeatedly arranged.

3. The film body according to claim 1 or 2, wherein dots are arranged at a constant pitch in the array axis a1 of the first rhombic lattice region and the array axis a2 of the second rhombic lattice region.

4. The film body according to claim 3, wherein the dot pitches of the array axis a1 of the first rhombic lattice region and the array axis a2 of the second rhombic lattice region are equal.

5. A film body according to any one of claims 1 to 4, wherein the distance L1 between adjacent array axes a1 in the first rhombic lattice region is equal to the distance L2 between adjacent array axes a2 in the second rhombic lattice region.

6. A film body according to any one of claims 1 to 5, wherein the number of arrangement axes a1 in the first orthorhombic lattice region is equal to the number of arrangement axes a2 in the second orthorhombic lattice region.

7. A film body according to any one of claims 1 to 6, wherein the number of arrangement axes a1 in the first orthorhombic lattice region and the number of arrangement axes a2 in the second orthorhombic lattice region are 4 or less.

8. The film body according to any one of claims 1 to 7, wherein the array axis a1 is parallel to the longitudinal direction of the film body.

9. A film body according to any one of claims 1 to 8, wherein the dot fillers have optical functions and function as an optical film.

10. The film body according to any one of claims 1 to 8, wherein the dot structure is a nanostructure formed as a recess or protrusion arranged on a transparent substrate.

11. A method for manufacturing a film body in which dots are arranged in a pseudo-random dot pattern in the xy plane, To form a pseudo-random dot pattern, a first rhombic lattice region is formed in which multiple dot array axes a1, where dots are arranged at a predetermined pitch in the x-direction, are arranged in the b-direction at an angle α (excluding 90°) oblique to the x-direction, and a second rhombic lattice region is formed in which multiple dot array axes a2, where dots are arranged at a predetermined pitch in the x-direction, are arranged in the c-direction, which is the inverse of the b-direction with respect to the x-direction. These regions are repeatedly arranged at predetermined intervals in the y-direction, such that the extensions of the array axes in the b-direction of the first rhombic lattice region do not become the array axes of the second rhombic lattice region. In the array axis a1 of the adjacent first rhombic lattice region and the array axis a2 of the second rhombic lattice region, the nearest dots are arranged such that their positions are offset in the x-direction. A dot is a tiny point or structure arranged in a pseudo-random dot pattern. The aforementioned structure is convex, raised, concave, recessed, or concave-convex, A method for manufacturing a film body, wherein the aforementioned minute dots are fillers arranged in a resin layer.

12. A structure in which dots are arranged in a pseudo-random dot pattern in the xy plane, In the pseudo-random dot pattern described above, a first rhombic lattice region is formed in which multiple dot array axes a1, where dots are arranged at a predetermined pitch in the x-direction, are arranged obliquely in the b-direction at an angle α (excluding 90°) to the x-direction, and a second rhombic lattice region is formed in which multiple dot array axes a2, where dots are arranged at a predetermined pitch in the x-direction, are arranged in the c-direction, which is the inverse of the b-direction with respect to the x-direction. These regions are repeatedly arranged at predetermined intervals in the y-direction, without the extension of the array axes in the b-direction of the first rhombic lattice region becoming the array axes of the second rhombic lattice region. In the array axis a1 of the adjacent first rhombic lattice region and the array axis a2 of the second rhombic lattice region, the positions of the nearest dots are shifted in the x-direction. A dot is a tiny point or structure arranged in a pseudo-random dot pattern. The aforementioned structure is convex, raised, concave, recessed, or concave-convex, A structure in which the aforementioned minute dots are fillers arranged in a resin layer.

13. The structure according to claim 12, wherein a first rhombic lattice region and a second rhombic lattice region are alternately and repeatedly arranged.

14. The structure according to claim 12 or 13, wherein dots are arranged at a constant pitch in the array axis a1 of the first rhombic lattice region and the array axis a2 of the second rhombic lattice region.

15. The structure according to claim 14, wherein the dot pitches of the array axis a1 of the first rhombic lattice region and the array axis a2 of the second rhombic lattice region are equal.

16. The structure according to any one of claims 12 to 15, wherein the distance L1 between adjacent array axes a1 in the first rhombic lattice region is equal to the distance L2 between adjacent array axes a2 in the second rhombic lattice region.

17. The structure according to any one of claims 12 to 16, wherein the number of array axes a1 in the first rhombic lattice region is equal to the number of array axes a2 in the second rhombic lattice region.

18. The structure according to any one of claims 12 to 17, wherein the number of array axes a1 in the first rhombic lattice region and the number of array axes a2 in the second rhombic lattice region are 4 or less.

19. The structure according to any one of claims 12 to 18, wherein the dot filler has an optical function.

20. The structure according to any one of claims 12 to 18, wherein the dot structure is a nanostructure formed as a recess or protrusion arranged on a transparent substrate.

21. The structure according to any one of claims 12 to 18, wherein the dot structure is a microlens and functions as a dot projector.

22. A method for manufacturing a structure in which dots are arranged in a pseudo-random dot pattern in the xy plane, In a pseudo-random dot pattern, a first rhombic lattice region is formed in which multiple dots are arranged in the b direction at an angle α (excluding 90°) to the x direction, with dots arranged at a predetermined pitch in the x direction along an array axis a1. A second rhombic lattice region is formed in which multiple dots are arranged in the c direction, which is the inverse of the b direction with respect to the x direction, with dots arranged at a predetermined pitch in the x direction along an array axis a2. These regions are repeatedly arranged at predetermined intervals in the y direction, such that the extension of the array axis in the b direction of the first rhombic lattice region does not become the array axis of the second rhombic lattice region. In adjacent array axes a1 of the first rhombic lattice region and array axis a2 of the second rhombic lattice region, the nearest dots are arranged such that their positions are shifted in the x direction. A dot is a tiny point or structure arranged in a pseudo-random dot pattern. The aforementioned structure is convex, raised, concave, recessed, or concave-convex, A method for manufacturing a structure, wherein the aforementioned minute dots are fillers arranged in a resin layer.

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