Concave polygonal aperture corner cube prism and method

Abstract

A concave polygonal aperture corner cube prism and a method for providing the same. [Solution] A retroreflective structure having a plurality of corner cube prisms in a sheet and at least one projection aperture of the corner cube prisms having a concave polygonal shape with at least one interior angle greater than 180°. Furthermore, examples of this technology may be advantageously comprised of: different shapes such as truncated cubes, cuboids, chevron cubes, or stretched chevron cubes; sizes such as 25 microns to 500 microns; directions such as unidirectional, bidirectional, or a combination thereof; inclination such as -20° to +20°; vertex center positions; and / or tiling such as in situ, parquet, or a combination thereof to further customize the optical retroreflective performance.

Description

Technical Field

[0001] Field This application claims the benefit of U.S. Patent Application No. 17 / 514,934, filed Oct. 29, 2021, the content of which is hereby incorporated by reference in its entirety.

[0002] This technology generally relates to corner cube prisms, and more particularly to retroreflective prisms having a projection aperture shape of a concave polygon and methods thereof.

Background Art

[0003] Background Retroreflective materials are designed to reflect incident radiation either back towards the source emitter or substantially back, regardless of the angle of incidence. Triangular and rectangular corner cube retroreflectors are the most common retroreflective technologies for high-performance applications at the current state of the art.

[0004] All known corner cube prism types with projection aperture shapes that are commercially available or described in the literature are convex polygons (i.e., all interior angles of the projection aperture polygon are less than 180°). For example, triangles, rectangles, and hexagons.

[0005] Prism tilt (also known as bevel) is described as an example in the specification of U.S. Patent No. 3,923,378 (Patent Document 1) by Heenan and the specification of U.S. Patent No. 4,588,258 (Patent Document 2) by Hoopman, which are hereby incorporated by reference in their entirety. The "cube axis" is defined as the axis that coincides with the cube vertex where all three facet planes of the prism are symmetrically arranged around it. Referring to FIG. 1, the tilt is the angle between the normal to the plane of the optical medium and the cube axis. The rule adopted is that a positive tilt corresponds to a prism rotation where the "C" facet becomes more parallel to the plane of the optical material.

Prior Art Documents

[0006] [Patent Document 1] U.S. Patent No. 3,923,378 [Patent Document 2] Portugal No. 4,588,258 [Overview of the Initiative] [Means for solving the problem]

[0007] overview A retroreflective structure comprising a plurality of corner cube prisms within a sheet, and at least one projection aperture of the corner cube prism having a concave polygonal shape with at least one interior angle greater than 180°.

[0008] A method for manufacturing a retroreflective structure includes providing a sheet for the retroreflective structure. A plurality of corner cube prisms are formed within the sheet, and at least one of the corner cube prisms has a projection aperture formed to have a concave polygonal shape with at least one interior angle greater than 180°.

[0009] Examples of this technology offer many advantages, including the provision of improved, customizable retroreflective structures. In examples of this technology, at least one projected polygonal aperture shape of the prisms is concave, and at least one interior angle of the projected aperture polygon is greater than 180°. Furthermore, examples of this technology may advantageously consist of: different shapes such as truncated cubes, cuboids, chevron cubes, or stretched chevron cubes; sizes such as 25 μm to 500 μm; directions such as unidirectional, bidirectional, or a combination thereof; inclination such as -20° to +20°; vertex center position; and / or tiling such as in situ, parquet, or a combination thereof, for further customization of optical retroreflective performance. In addition, each individual prism in the prism ensemble may have an inherently defined inclination that provides additional degrees of freedom to achieve the target aggregated photometric performance. The present invention provides, for example, the following items: (Item 1) It is a retroreflective structure, Multiple corner cube prisms within the sheet, At least one projection aperture of the corner cube prism having a concave polygonal shape with at least one interior angle greater than 180° and A retroreflective structure equipped with this feature. (Item 2) The inclination of each cubic axis of the corner cube prism with respect to the normal of the plane extending along the sheet is between -20° and +20°. The structure described in item 1, further including the above. (Item 3) The structure described in item 2, wherein the aforementioned inclination is approximately +9.8°. (Item 4) The dihedral angle deviation of at least one facet of the corner cube prism is within ±1° of each other. The structure described in item 1, further including the above. (Item 5) The structure according to item 1, wherein at least one of the corner cube prisms has a projection aperture that further includes a chevron shape. (Item 6) The structure according to item 5, wherein one dimension of the chevron shape is elongated compared to the other dimensions of the chevron shape. (Item 7) The structure according to item 1, wherein each of the corner cube prisms has the same orientation. (Item 8) The structure according to item 1, wherein the sheet includes at least one of a unidirectional or bidirectional arrangement of the corner cube prism. (Item 9) The structure according to item 8, wherein the cubic axis of each corner cube prism with respect to the normal of the plane extending along the sheet is between -20° and +20°. (Item 10) The structure described in item 8, wherein each vertex of the corner cube prism is offset from the center. (Item 11) The structure according to item 1, wherein the sheet comprises a plurality of tiles, each having a plurality of the corner cube prisms, and the tiles are arranged in alternating angular directions. (Item 12) The structure according to item 11, wherein the plurality of tiles on the sheet are at least partially formed in situ. (Item 13) The structure according to item 11, wherein the plurality of tiles on the sheet are at least partially parqueted together. (Item 14) The structure described in item 1, wherein the corner cube prism has a prism pitch range of 25 μm to 500 μm. (Item 15) The sheet comprises a plurality of tiles, each having a plurality of the corner cube prisms, In one or more of the aforementioned tiles, the inclination of two or more cubic axes of the corner cube prism with respect to the normal of the plane extending along the sheet is different from that of the other. The structure described in item 1. (Item 16) A method for manufacturing a retroreflective structure, The steps include providing a sheet for the retroreflective structure, A step of forming a plurality of corner cube prisms within the sheet, further comprising forming a projection aperture of at least one of the corner cube prisms such that it has a concave polygonal shape having at least one interior angle greater than 180°, and Methods that include... (Item 17) The inclination of each cubic axis of the corner cube prism with respect to the normal of the plane extending along the sheet is between -20° and +20°. The method described in item 16, further including the method described in item 16. (Item 18) The method according to item 17, wherein the aforementioned incline is approximately +9.8°. (Item 19) The dihedral angle deviation of at least one facet of the corner cube prism is within ±1° of each other. The method described in item 16, further including the method described in item 16. (Item 20) The method according to item 16, wherein at least one of the corner cube prisms the projection aperture further includes a chevron shape. (Item 21) The method according to item 20, wherein one dimension of the chevron shape is elongated compared to the other dimensions of the chevron shape. (Item 22) The method according to item 16, wherein each of the corner cube prisms has the same orientation. (Item 23) The method according to item 16, wherein the sheet includes at least one of a unidirectional or bidirectional arrangement of the corner cube prism. (Item 24) The method according to item 23, wherein the cubic axis of each corner cube prism with respect to the normal of the plane extending along the sheet is -20° to +20°. (Item 25) The method described in item 23, wherein each vertex of the cube in the aforementioned corner cube prism is offset from the center. (Item 26) The method according to item 16, wherein the sheet comprises a plurality of tiles, each having a plurality of the corner cube prisms, and the tiles are arranged in alternating angular directions. (Item 27) The method according to item 26, wherein the plurality of tiles on the sheet are at least partially formed in situ. (Item 28) The method according to item 26, wherein the plurality of tiles on the sheet are at least partially parqueted together. (Item 29) The method according to item 16, wherein the corner cube prism has a prism pitch range of 25 μm to 500 μm. (Item 30) The sheet comprises a plurality of tiles, each having a plurality of the corner cube prisms, In one or more of the aforementioned tiles, the inclination of two or more cubic axes of the corner cube prism with respect to the normal of the plane extending along the sheet is different from that of the other. The method described in item 16. [Brief explanation of the drawing]

[0010] [Figure 1] This is a perspective view of a prism showing illustrative definitions of facets A, B, and C, as well as the inclination as the angle between the normal to the plane of the optical medium and the cubic axis. [Figure 2] This is a perspective view of an exemplary prism having a chevron shape within a sheet of retroreflective structure. [Figure 3] This figure shows effective area plots for an exemplary truncated cube at different angles of incidence. [Figure 4] This figure shows the effective area plots of an exemplary rectangular prism at different angles of incidence. [Figure 5] This figure shows the effective area plots of an exemplary chevron cube at different angles of incidence. [Figure 6] This figure shows the effective area plots of an exemplary stretched chevron cube at different angles of incidence. [Figure 7] This graph provides an illustrative comparison of the effective area of ​​a truncated cube, cuboid, chevron cube, and elongated chevron cube, each arranged in a first orientation. [Figure 8] This graph provides an illustrative comparison of the effective area of ​​truncated cubes, rectangular prisms, chevron cubes, and elongated chevron cubes, each arranged in alternating orientations. [Figure 9] This is a diagram of an exemplary sheet of retroreflective structure arranged by bidirectional chevron tiling. [Figure 10] This is a diagram illustrating an exemplary sheet of a retroreflective structure having unidirectional chevron tiling. [Figure 11] This is a diagram of an exemplary sheet of a retroreflective structure with a mixture of unidirectional and bidirectional chevron tiling. [Figure 12] This is a diagram of an exemplary sheet of a retroreflective structure having a corner cube prism, each comprising a chevron cube with a 5° inclination. [Figure 13] This is a diagram of an exemplary sheet of a retroreflective structure having a corner cube prism, each comprising a chevron cube with a 12° inclination. [Figure 14] This is a diagram of an exemplary sheet of a retroreflective structure having unidirectional chevron tiling with a 0° inclination and eccentric vertices. [Figure 15] This is an exemplary perspective view of a prism showing a combined tilt angle. [Figure 16] This is a diagram of an exemplary sheet of a retroreflective structure having chevron cube tiling with compound inclination angles. [Figure 17] This is a diagram of an exemplary sheet of a retroreflective structure having an insitu tiling of 0 / 90. [Figure 18] This is a diagram of an exemplary sheet of retroreflective structure having 0 / 90 parquet tiling. [Figure 19] This is a diagram of an exemplary sheet of retroreflective structure having 0 / 90 in situ tiling and parquet tiling. [Figure 20] This is a diagram of an exemplary sheet of a retroreflective structure having parquet tiling with various orientation angles. [Figure 21] This is a diagram of an exemplary sheet of a retroreflective structure having parquet tiling using chevron cubes with different inclines. [Figure 22] This is a diagram of an exemplary sheet of a retroreflective structure whose inclination changes in situ. [Modes for carrying out the invention]

[0011] Detailed explanation Various examples of sheets of retroreflective structure 10(1)-10(13) having prisms with projection apertures having a concave polygonal shape with at least one interior angle greater than 180° are shown in Figures 9-14 and 16-22. In these examples, the sheets of retroreflective structure 10(1)-10(13) have prisms having: different shapes such as truncated cubes, cuboids, chevron cubes, or stretched chevron cubes; sizes such as 25 μm to 500 μm; directions such as unidirectional, bidirectional, or a combination thereof; inclination such as -20° to +20°; vertex center position; and / or tiling such as in situ, parquet, or a combination thereof. Examples of this technique offer many advantages, including the provision of improved and customizable retroreflective structures.

[0012] Referring more specifically to Figure 2, an example of a corner cube prism 12(3) having a projected polygonal aperture which is a chevron-like concave polygon shape with at least one interior angle greater than 180° is shown. In this example, the corner cube prism 12(3) has a cubic axis that is tilted at +9.8° with respect to the normal of the plane extending along the sheet on which the corner cube prism is located, but the corner cube prism can have other shapes and / or other tilts, such as a tilt of -20° to +20°, for example.

[0013] Furthermore, in this example, the corner cube prism 12(3) has facets A, B, and C 14(1)-14(3) and dihedral edges A, B, and C 16(1)-16(3). The dihedral angle deviation (DAD) is the amount by which each of facets A, B, and C 14(1)-14(3) deviates from a perfect 90° interior angle with respect to an adjacent facet among facets A, B, and C 14(1)-14(3). Thus, the corner cube prism 12(3) has three DADs, which are specified for facets A, B, and C 14(1)-14(3). Furthermore, examples of this technique may include each individual prism in an ensemble of prisms on a sheet of retroreflective structures, each having a DAD of the facets of each prism, thereby achieving specific design objectives as illustrated and described herein and disclosed as an example in Table 1 of column 5 of U.S. Patent No. 5,138,488 by Szczech, which is incorporated herein by reference in its entirety.

[0014] As illustrated in U.S. Patent No. 4,588,258 by Hoopman, adjusting the tilt angle changes the angle of incidence at which peak brightness is achieved. This example of the technique utilizes this adjustment, along with further dynamically customized modifications, to optimize the effective geometric area at each prism within the sheet of exemplary retroreflective structures 10(1)-10(13).

[0015] In these examples, the triple-reflected ray path defining retroreflection determines the amount of light energy available for distribution to a specific target photometric performance. If all incident rays are well mapped to three-bounce retroreflected exit rays, the prism has 100% effective area. For all incident rays that do not retroreflect well due to the lack of facets as part of their ray path (or inability to perform total internal reflection (TIR), as can occur with airbag retroreflectors), the effective area is considered to be reduced. Thus, an example of the claimed technology is the effective area (A a ) is defined as follows: [ka] In the equation, A0 is the projected prism incident aperture area, and A1 is the effective area of ​​the prism facets supporting the three bounce retroreflections.

[0016] Referring to Figures 3–6, the effective areas of various examples of corner cube prisms 12(1)–12(4) of different shapes at incident angles β of -40°, -20°, 0°, +20°, and +40° are shown. In each plot, the projected aperture at the mentioned incident angle is shown, with areas supporting retroreflection shown unhidden, while areas not supporting retroreflection are shown in shaded areas. These examples illustrate how prisms 12(1)–12(4) appear under different illumination conditions. Referring to Figures 7–8, graphs of effective area versus incident angle are shown for each of the examples of corner cube prisms 12(1)–12(4) of different shapes. Thus, as shown by these examples, the prisms in the sheet of examples of retroreflective structures 10(1)–10(13) may have aspects such as shape and / or inclination that are tuned as examples to customize photometric performance as required for specific applications.

[0017] As shown in Figures 3, 5, and 7-8, the significant advantages of the chevron cube-shaped prism 12(3) versus the truncated cube-shaped prism 12(1) are demonstrated. Furthermore, as shown in Figures 4, 5, and 7-8, as the angle of incidence increases, the chevron cube-shaped prism 12(3) and the rectangular parallelepiped-shaped prism 12(2) become very similar in terms of available effective area. Moreover, as shown in Figures 6-8, the effective area of ​​the chevron cube can be further increased by "extending" the aperture, as in prism 12(4), so that it converges toward the effective area characteristics of the rectangular parallelepiped. In this example, facet 14(3) of prism 12(3) is elongated compared to facets 14(1) and 14(2) of A and B. In this configuration of prism 12(4), as shown in Figure 6, the ineffective optical region consumes less of the total prism region, thereby increasing the overall effective area.

[0018] Referring to Figures 9–11, exemplary sheets of retroreflective structures 10(1)–10(3) arranged by chevron tiling in different directions are shown, but one or more of these retroreflective structures may have one or more corner cube prisms having other selected shapes, such as those shown in Figures 3–6, for example, to be customized for specific photometric performance. In these examples, retroreflective structures 10(1)–10(3) utilize corner cube prisms 12(3) having chevron-shaped projection apertures. These corner cube prisms 12(3) having chevron-shaped projection apertures have the characteristic that they can be tiled bidirectionally as shown in Figure 9, or completely unidirectionally as shown in Figure 10. In the bidirectional configuration of the exemplary sheet of retroreflective structure 10(1) shown in Figure 9, all corner cube prisms 12(3) having “upper chevron”-shaped projection apertures are paired with another adjacent corner cube prism 12(3) rotated 180° relative to have a “lower chevron”-shaped projection aperture. In the unidirectional configuration of the exemplary sheet of retroreflective structure 10(2) shown in Figure 10, all corner cube prisms 12(3) having chevron-shaped projection apertures are oriented in the same direction. Referring to Figure 11, an exemplary sheet of retroreflective structure 10(3) is shown having mixed unidirectional and bidirectional configurations of corner cube prisms 12(3) having chevron tiling of chevron-shaped projection apertures, which can result in a progressively improved effective area due to the adjacent continuity of the C facets 14(3), although other configurations of mixed unidirectional and bidirectional configurations of corner cube prisms 12(3) may be used.

[0019] In the unidirectional configuration of the exemplary sheet of the retroreflective structure 10(2) shown in Figure 10, prims having a chevron cube shape as shown in Figure 5 have a significant advantage for high incident angles as shown in Figure 7. To ensure that the orientation of the prism sheet is not a concern, bidirectional or pseudo-bidirectional prism sheets, such as the exemplary sheet of the retroreflective structure 10(3) shown in Figure 11, may be manufactured with an effective area as shown in Figure 8.

[0020] In this example of the technique, the advantageous geometric shape is a chevron shape, where the prism inclination is as follows: [ka] This occurs when it is equal to, and this [ka] The value will be...

[0021] By adjusting the inclination, various other chevron aperture shapes with different photometric performance characteristics appear. For example, the inclination may be less than 9.7°, e.g., 5°, for each prism 12(3) in the sheet of retroreflective structure 10(4) as shown in Figure 12, or greater than 9.7°, e.g., 12°, for each prism 12(3) in the sheet of retroreflective structure 10(5) as shown in Figure 13. In this example of the technique, the inclination angle of the optical axis of the prisms in the sheet of retroreflective structure is typically in the range of -20° to +20° to obtain several desirable photometric performance characteristics.

[0022] In another example of this technique, the tilt of the prisms may be adjusted (or may be zero) while maintaining a pure chevron aperture shape by offsetting the cubic vertex positions of each prism for unidirectional tiling, as shown in the sheet of retroreflective structure 10(6) in Figure 14. In this example, moving the cubic vertex positions of each prism from the center results in a peak effective area being achieved at non-zero incidence angles. In this way, the performance can be adjusted again in another way that is maximized with respect to positive or negative incidence angle situations.

[0023] In other examples of this technology, the tilt of the retroreflective structure must be applied conventionally in the vertical direction, as exemplified in retroreflective structures 10(4) and 10(5). In other examples, the retroreflective structure 10(7) may be customized by applying a deviation to the cubic axis in the horizontal plane so that the composite tilt angle is achieved as shown in Figures 15 and 16. In examples of this technology, the composite tilt angle for retroreflective applications can be customized within the range of -20° to +20° to achieve one or more desired photometric characteristics.

[0024] Referring to Figures 17–21, various rotations and inclinations are shown for other exemplary retroreflective structures 10(8)–10(13) for manufacturing and performance purposes. For example, as shown in Figure 17, a chevron-shaped prism 12(3) may be tiled “in situ” in 0° and 90° orientations of exemplary retroreflective structure 10(8) as part of the prism machining process. Alternatively, as shown in Figure 18, individual prism plates 18(1)–18(4) may be manufactured and then parqueted together to form a sheet for exemplary retroreflective structure 10(9). In another example, both methods may be combined by parqueting prisms tiled in situ to form a sheet for exemplary retroreflective structure 10(10), as shown in Figure 19. In yet another example, the prism tiling does not need to be constrained to 0° and 90° orientations, and may have various orientation angles to form a sheet for the exemplary retroreflective structure 10(11) as shown in Figure 20. Furthermore, in yet another example, different prism inclinations, and even different prism types, may be tiled to form a sheet for the exemplary retroreflective structure 10(12), as shown in Figure 21. Moreover, in the exemplary retroreflective structure 10(13) shown in Figure 22, advantageously, the inclinations of the individual prisms in the tile may be modified in situ so that the array of prisms includes multiple inclination rules. In this way, additional design degrees of freedom can be applied to optimize the performance of the prism array. Adjusting the inclination changes the shape of the individual prism apertures in the array, making countless possible prism inclinations available. Such inclinations may be selected to optimize the chosen machining technique, or to maximize the effective area, or to produce a preferred surface appearance or other criterion.

[0025] The illustrations and the examples described above are illustrative, and various other permutations of these examples may be applied. Furthermore, other examples of the claimed technology may have other prism shapes, tilings, and / or rotational permutations. In addition, various different types of manufacturing processes may be used to form these prisms, such as fly-cutting, micro-chiseling, milling, pin-banding, and / or lithography.

[0026] Accordingly, examples of this art, as illustrated and described in the examples herein, provide improved, customizable retroreflective structures. In examples of this art, at least one projection polygonal aperture shape of the prism is concave, and at least one interior angle of the projection aperture polygon is greater than 180°. Furthermore, examples of this art may advantageously consist of: different shapes such as truncated cubes, cuboids, chevron cubes, or stretched chevron cubes; sizes such as 25 μm to 500 μm; directions such as unidirectional, bidirectional, or a combination thereof; inclination such as -20° to +20°; vertex center position; and / or tiling such as in situ, parquet, or a combination thereof, for further customization of optical retroreflective performance.

[0027] Having thus described the basic concepts of the present invention, it will be apparent to those skilled in the art that the detailed disclosures described herein are intended to be merely illustrative and not limiting. Various alternatives, improvements, and modifications, not expressly stated herein, are intended to those skilled in the art. These alternatives, improvements, and modifications are intended to be suggested herein and are within the spirit and scope of the present invention. Therefore, the order in which processing elements or sequences are described, or the use of numbers, letters, or other names, is not intended to limit the processes described in the claims to any particular order, except as may be specified in the claims. Accordingly, the present invention is limited only by the following claims and their equivalents.

Claims

1. A structure for a retroreflector, wherein the structure is: Multiple corner cube prisms within the sheet, At least one aperture among the plurality of corner cube prisms and Equipped with, The opening comprises a plurality of facets and a concave polygonal shape having at least one interior angle greater than 180°, wherein each of the plurality of facets extends continuously along only one plane from each intersection of the plurality of facets in the opening to the opening entrance.

2. The structure according to claim 1, wherein the inclination of each cubic axis of the plurality of corner cube prisms with respect to the normal of a plane extending along the sheet is -20° to +20°.

3. The structure according to claim 2, wherein the inclination is approximately +9.8°.

4. The structure according to claim 1, wherein the dihedral angle deviation of each of the at least one of the plurality of facets of the plurality of corner cube prisms is within ±1° of each other.

5. The structure according to claim 1, wherein at least one of the plurality of corner cube prisms has a chevron shape.

6. The structure according to claim 5, wherein one dimension of the chevron shape is elongated compared to the other dimensions of the chevron shape.

7. The structure according to claim 1, wherein each of the plurality of corner cube prisms has the same orientation.

8. The structure according to claim 1, wherein the sheet includes at least one of a unidirectional or bidirectional arrangement of the plurality of corner cube prisms.

9. The structure according to claim 8, wherein the cubic axis of each of the plurality of corner cube prisms with respect to the normal of a plane extending along the sheet is -20° to +20°.

10. The structure according to claim 8, wherein the vertices of each of the multiple corner cube prisms are offset from the center.

11. The structure according to claim 1, wherein the sheet comprises a plurality of tiles, each of the plurality of tiles comprises the plurality of corner cube prisms, and the plurality of tiles are oriented at alternating angles.

12. The structure according to claim 11, wherein the plurality of tiles on the sheet are at least partially parqueted together.

13. The structure according to claim 1, wherein the plurality of corner cube prisms have a prism pitch range of 25 μm to 500 μm.

14. The sheet comprises a plurality of tiles, each of the plurality of tiles comprises the plurality of corner cube prisms, The structure according to claim 1, wherein in one or more of the plurality of tiles, the inclination of two or more cubic axes of the plurality of corner cube prisms with respect to the normal of the plane extending along the sheet is different from that of the plurality of tiles.

15. A method for manufacturing a retroreflector structure, wherein the method is: To provide a sheet for the structure of the retroreflector, To form multiple corner cube prisms within the aforementioned sheet Includes, The method further comprises forming an opening in the plurality of corner cube prisms such that it comprises a plurality of facets and a concave polygonal shape having at least one interior angle greater than 180°, wherein each of the plurality of facets extends continuously along a single plane from each intersection of the plurality of facets in the opening to the opening entrance.

16. The method according to claim 15, wherein the inclination of each cube axis of the plurality of corner cube prisms with respect to the normal of a plane extending along the sheet is -20° to +20°.

17. The method according to claim 16, wherein the inclination is approximately +9.8°.

18. The method according to claim 17, wherein the dihedral angle deviation of each of the at least one of the plurality of facets of the plurality of corner cube prisms is within ±1° of each other.

19. The method according to claim 15, wherein at least one of the plurality of corner cube prisms further includes a chevron shape.

20. The method according to claim 19, wherein one dimension of the chevron shape is elongated compared to the other dimensions of the chevron shape.

21. The method according to claim 15, wherein each of the plurality of corner cube prisms has the same orientation.

22. The method according to claim 15, wherein the sheet includes at least one of the unidirectional or bidirectional arrangements of the plurality of corner cube prisms.

23. The method according to claim 22, wherein the cubic axis of each of the plurality of corner cube prisms with respect to the normal of a plane extending along the sheet is -20° to +20°.

24. The method according to claim 22, wherein each of the cube vertices of the plurality of corner cube prisms is offset from the center.

25. The method according to claim 15, wherein the sheet comprises a plurality of tiles, each of the plurality of tiles comprises the plurality of corner cube prisms, and the plurality of tiles are oriented at alternating angles.

26. The method according to claim 25, wherein the plurality of tiles on the sheet are at least partially parqueted together.

27. ​​The method according to claim 15, wherein the plurality of corner cube prisms have a prism pitch range of 25 μm to 500 μm.

28. The sheet comprises a plurality of tiles, each of the plurality of tiles comprises the plurality of corner cube prisms, The method according to claim 15, wherein in one or more of the plurality of tiles, the inclination of two or more cubic axes of the plurality of corner cube prisms with respect to the normal of a plane extending along the sheet is different from that of the plurality of tiles.

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