Aerial image formation element

Abstract

An aerial image formation element according to the present embodiment comprises a plurality of columnar reflectors disposed along a reference plane which includes a first direction and a second direction that is orthogonal to the first direction. The columnar reflectors each have a central axis which is parallel to a third direction that orthogonal to the reference plane and each have a first end surface that is on a first side in the third direction, a second end surface that is on a second side opposite from the first side in the third direction, and side surfaces that connect the first end surface and the second end surface along the third direction. The columnar reflectors each have a columnar body that comprises a transparent material which is transparent with respect to incident light, a first light-shielding layer that is provided at the first end surface, a second light-shielding layer that is provided at the second end surface, and a reflection layer that is provided to a reflection region of the side surfaces and that reflects light which propagates inside the columnar body. The shape of the columnar body in a cross-section including the first direction and the third direction is a trapezoid which gets narrower toward the first side in the first direction.

Description

Aerial image forming element

[0001] The present invention relates to an aerial image forming element.

[0002] Conventionally, aerial imaging elements have been proposed that refract and reflect light emitted from a light source to form a real image, i.e., an aerial image, in the air. One example of an aerial imaging element is a retrotransmissive optical element. A retrotransmissive optical element forms an aerial image at a position that is plane-symmetrical to the light source relative to the element. One example of a retrotransmissive optical element is a micromirror array plate (MMAP), in which two mirrors act as corner reflectors. When forming an aerial image using an MMAP, the aerial image must be observed along the direction in which the light emitted from the light source is retrotransmitted by the two mirrors. This significantly limits the viewing angle in a direction horizontal to the reference plane on which the two mirrors are arranged, potentially resulting in the loss of part of the aerial image or a reduction in the brightness of the aerial image depending on the direction from which the aerial image is observed.

[0003] In order to improve the problem of the significant limitation of the horizontal viewing angle of an aerial image when using MMAP as described above, an optical element has been proposed that includes a plurality of reflective elements, each having a reflective surface on at least a portion of the side surface of a cylinder or column. The plurality of reflective elements are arranged on a plate-like member such as a panel. The reflective surfaces of the reflective elements are perpendicular to the plate surface of the panel. With the plurality of reflective elements, light incident from any horizontal direction is reflected by the side surfaces, so there is no limitation on the horizontal viewing angle of the aerial image. However, with the proposed optical element as described above, only light that is reflected only once by the side surface of the cylinder or column contributes to image formation, and light incident on the cylinder or column other than light passing through the central axis is not retroreflected, resulting in an observable aerial image.

[0004] Patent Document 1 discloses an aerial image forming element including a plurality of light-transmitting cylinders. In the aerial image forming element disclosed in Patent Document 1, the plurality of cylinders are arranged two-dimensionally so that the two parallel end faces of each cylinder are positioned in the same plane. In the aerial image forming element disclosed in Patent Document 1, incident light is collected through each cylinder, so that a real image is formed in the air, and an observable aerial image is obtained.

[0005] Japanese Patent Application Publication No. 2016-090826

[0006] The aerial imaging element disclosed in Patent Document 1 addresses the resolution required for an aerial image, but due to the spacing between adjacent cylinders among the multiple cylinders, there are limitations to further improving the resolution of the aerial image. In the aerial imaging element disclosed in Patent Document 1, the total area of ​​the light-exiting end faces of the multiple cylinders occupies a large area in the observer's field of view. Light emitted from the interior of each cylinder to the outside through the light-exiting end face of the cylinder does not contribute to the formation of the aerial image. Each end face of the light-exiting end of the cylinder is provided with a light-blocking section to block light. Therefore, with the aerial imaging element disclosed in Patent Document 1, the amount of light reaching the observer's eye within the observer's field of view is low, potentially resulting in a dark aerial image. For these reasons, there is a demand for an aerial imaging element that can further improve the resolution of the aerial image and increase the amount of light reaching the observer's eye.

[0007] An aerial image forming element according to an embodiment of the present invention includes a plurality of columnar reflectors arranged along a reference plane including a first direction and a second direction orthogonal to the first direction. Each of the columnar reflectors has a central axis parallel to a third direction orthogonal to the reference plane, a first end face on a first side in the third direction, a second end face on a second side opposite the first side in the third direction, and a side surface connecting the first end face and the second end face along the third direction, the columnar reflector being made of a transparent material that is transparent to incident light, a first light-shielding layer provided on the first end face and blocking light from outside the columnar body, a second light-shielding layer provided on the second end face and blocking light from outside the columnar body, and a reflective layer provided in a reflective region of the side surface and reflecting light propagating inside the columnar body. The shape of a cross section of the columnar body including the first direction and the third direction is a trapezoid that narrows toward the first side in the first direction. The reflective area is an area on the side surface on a first side in the first direction from a position on the side surface that is the same as the central axis in the first direction when viewed from the third direction.

[0008] According to the present invention, it is possible to provide an aerial image forming element that can increase the resolution of an aerial image and the amount of light of the aerial image that reaches the observer's eyes.

[0009] 1. It is a perspective view of an aerial image forming element of one embodiment of the present invention. It is a perspective exploded view of a columnar reflector of the aerial image forming element shown in FIG. 1. It is a side view of a columnar reflector of the aerial image forming element shown in FIG. 1. It is a cross-sectional view of a columnar reflector of the aerial image forming element shown in FIG. 1. It is a cross-sectional view of a columnar reflector of the aerial image forming element shown in FIG. 1. It is a side view for explaining the behavior of light in the aerial image forming element shown in FIG. 1. It is a cross-sectional view for explaining the behavior of light in the columnar reflector of the aerial image forming element shown in FIG. 1. It is a cross-sectional view for explaining the behavior of light in the columnar reflector of the aerial image forming element shown in FIG. 1. It is another perspective view of an aerial image forming element of one embodiment of the present invention. It is a perspective view of a conventional aerial image forming element. It is an image of an aerial image formed by an aerial image forming element of an example in an optical simulation. It is an image of an aerial image formed by an aerial image forming element of a comparative example in an optical simulation. It is a plan view of a modified example of the aerial image forming element shown in FIG. 1.

[0010] Hereinafter, an embodiment of the aerial image forming element of the present invention will be described with reference to the drawings.

[0011] First, the configuration of an aerial image forming element 10A according to one embodiment of the present invention will be described. FIG. 1 is a perspective view of the aerial image forming element 10A. As shown in FIG. 1, the aerial image forming element 10A includes a plurality of columnar reflectors 20. The plurality of columnar reflectors 20 are arranged along a reference plane VP including the D1 and D2 directions, which are orthogonal to each other. The plurality of columnar reflectors 20 are, for example, aligned in the D1 and D2 directions and are in contact with each other without any gaps in the D1 and D2 directions. In the D1 and D2 directions, the plurality of columnar reflectors 20 are arranged without any gaps, and the side surfaces of two adjacent columnar reflectors 20 are in contact with each other. In the aerial image forming element 10A according to this embodiment, the plurality of columnar reflectors 20 have the same shape, size, and configuration.

[0012] FIG. 2 is an exploded perspective view of the columnar reflector 20. FIG. 2 shows two columnar reflectors 20, 20 adjacent to each other in the D1 direction among the multiple columnar reflectors 20 included in the aerial image forming element 10A, and two columnar reflectors 20, 20 adjacent to each other in the D2 direction, disassembled in the D2 direction. FIG. 3 is a side view of the columnar reflector 20, viewed along the D2 direction. FIG. 4 is a cross-sectional view of the columnar reflector 20, showing the columnar reflector 20 cut along a plane including the D1 direction and the D3 direction. The D3 direction is orthogonal to the D1 direction and the D2 direction. As shown in FIGS. 2 to 4, the columnar reflector 20 has a columnar body 30, a light-shielding layer 41, a light-shielding layer 42, and a reflective layer 50.

[0013] In the following description, one side of the D1 direction will be referred to as the -D1 side, and the other side of the D1 direction will be referred to as the +D1 side. One side of the D2 direction will be referred to as the -D2 side, and the other side of the D2 direction will be referred to as the +D2 side. One side of the D3 direction will be referred to as the -D3 side, and the other side of the D3 direction will be referred to as the +D3 side.

[0014] The columnar body 30 has a central axis CX parallel to the D3 direction, and has a lower end face 31 on the −D3 side, an upper end face 32 on the +D3 side, and a side face 34. The side face 34 connects the end face 31 and the end face 32 in the D3 direction. The end face 32 is provided on the opposite side of the side face 34 in the D3 direction.

[0015] The columnar body 30 is made of a transparent material that is transparent to at least incident light, for example, a single transparent material. The transparent material of the columnar body 30 has a refractive index higher than that of the air outside the plurality of columnar reflectors 20. Examples of the transparent material of the columnar body 30 include optical glass and resin that is transparent in the visible wavelength range.

[0016] FIG. 4 is a diagram of the columnar reflector 20 cut at a plane including the central axis CX among planes including the D1 and D3 directions. As shown in FIG. 4, the cross-sectional shape of the columnar body 30 including the D1 and D3 directions is a trapezoid narrowing toward the -D1 side in the D1 direction. As the end face 31 moves from the -D1 side to the +D1 side in the D1 direction, it moves from the +D3 side to the -D3 side in the D3 direction. The end face 31 is flat in the D2 direction. As the end face 32 moves from the -D1 side to the +D1 side in the D1 direction, it moves from the -D3 side to the +D3 side in the D3 direction, moving away from the end face 31. The end face 32 is flat in the D2 direction. The height h1 in the D3 direction of the end on the -D1 side of the side face 34 is the smallest among the heights of the side face 34 in the D3 direction. The height h2 of the end of the side surface 34 on the +D1 side in the D3 direction is the largest among the heights of the side surface 34 in the D3 direction.

[0017] The cross-sectional shape of the columnar body 30, including the D1 and D2 directions, in the D3 direction between the end on the +D3 side of the end face 31 and the end on the −D3 side of the end face 32 is circular and approximately a perfect circle. The end faces 31 and 32 of the columnar body 30 have elliptical shapes, but the shape of the end faces 31 and 32 when viewed along the D3 direction is circular and approximately a perfect circle. The columnar body 30 is a member obtained by removing the end on the −D3 side in the D3 direction of a cylindrical member made of a transparent material and having the same radius and diameter as the radius r and diameter d of the columnar body 30 in the D1 and D2 directions, along a cut surface corresponding to the end face 31 that is inclined with respect to the D1 and D3 directions as described above, and removing the end on the +D3 side in the D3 direction of the cylindrical member along a cut surface corresponding to the end face 32 that is inclined with respect to the D1 and D3 directions as described above.

[0018] The light-shielding layer 41 is provided on the end surface 31 of the columnar body 30. The light-shielding layer 42 is provided on the end surface 32 of the columnar body 30. The light-shielding layers 41, 42 block light incident from outside the columnar reflector 20. As described above, the light-shielding layers 41, 42 are made of a material capable of blocking light incident from outside the columnar reflector 20, and are, for example, a chromium (Cr) mask.

[0019] FIG. 5 is a cross-sectional view of the columnar reflector 20, taken along line V-V in FIG. 4. Line V-V in FIG. 4 is a virtual line passing through the center plane of the columnar body 30 in the D3 direction. As shown in FIG. 5, the reflective layer 50 is provided in a reflective region RF of the side surface 34. When viewed along the D3 direction, the reflective region RF is a region on the -D1 side of a position RP1 on the side surface 34 of the columnar body 30 that is the same as the central axis CX in the D1 direction and on the -D2 side of the central axis CX, and a region on the -D1 side of a position RP2 on the side surface 34 that is the same as the central axis CX in the D1 direction and on the +D2 side of the central axis CX. The reflective region RF is a region from position RP1 in FIG. 5 in the circumferential direction centered on the central axis CX within a reference plane VP including the D1 and D2 directions, in the clockwise direction, that is, from position RP1 to position RP2 when the height of the side surface 34 in the D3 direction is first decreased and then increased. On the side surface 34, when viewed along the D3 direction, the region on the +D1 side in the D1 direction from positions RP1 and RP2, i.e., the region where the reflective layer 50 is not provided and the transparent material is exposed, is the transmissive region TF.

[0020] The reflective layer 50 reflects light propagating inside the columnar body 30. The reflective layer 50 is made of a material capable of reflecting light propagating inside the columnar body 30, and is a layer made of, for example, silver (Ag) or aluminum (Al).

[0021] Two of the plurality of columnar reflectors 20 that are adjacent to each other on the reference plane VP may be connected by a protrusion provided on the columnar body 30 of one of the columnar reflectors 20 and a recess formed on the columnar body 30 of the other columnar reflector 20 into which the protrusion can be inserted. Two columnar reflectors 20 that are adjacent to each other on the reference plane VP may be connected by a connecting member formed as a separate member from the two columnar reflectors 20. When a protrusion or recess is formed on the columnar body 30, the protrusion or recess is formed in a region where light does not propagate so that light propagating inside the columnar body 30 is not blocked by the recess or does not travel in an unexpected direction due to the protrusion or recess. The region NP in the columnar body 30 where light does not propagate will be described later.

[0022] FIG. 3 illustrates two columnar reflectors 20, 20 that are adjacent to each other and located furthest on the -D1 side in the D1 direction and furthest on the -D2 side in the D2 direction among the multiple columnar reflectors 20. For example, as shown in FIGS. 2 and 3, the multiple columnar reflectors 20, 20, ..., 20 arranged along the D1 direction at both ends in the D2 direction among the multiple columnar reflectors 20 are connected to each other by a connecting member 60. The connecting member 60 has an extending portion 61 and multiple protrusions 62. The extending portion 61 extends along the D1 direction and has a length in the D1 direction that corresponds to the total length in the D1 direction of one row of columnar reflectors 20 arranged along the D1 direction. The extending portion 61 has a side surface 61c on the +D2 side of the D2 direction and parallel to a plane including the D1 direction and the D3 direction. The protrusion 62 protrudes from the side surface 61c of the extending portion 61 toward the +D2 side in the D2 direction. The intervals between the multiple protrusions 62 in the direction D1 are, for example, equal to the diameter d of the columnar body 30 of the columnar reflector 20 .

[0023] As shown in FIG. 2, a recess 65 and a recess 66 are formed in the region NP of each columnar body 30 of a plurality of columnar reflectors 20 arranged along the D1 direction and disposed on the -D2 side in the D2 direction. In these columnar reflectors 20, when viewed from the D3 direction, the recess 65 is formed in an appropriate portion on the -D2 side of the central axis CX of the region NP of the columnar body 30. When viewed along the D2 direction, the shape of the opening of the recess 65 is the same as that of the protrusion 62. The recess 65 is formed so that at least the tip of the protrusion 62 of the connecting member 60 can be inserted from the -D2 side along the D2 direction and can be removed to the -D2 side. When viewed from the D3 direction, the recess 66 is formed in an appropriate portion on the +D2 side of the central axis CX of the region NP of the columnar body 30. The multiple protrusions 62 of the connecting member 60 are inserted from the -D2 side in the D2 direction into the recesses 65 of the columnar bodies 30 of the multiple columnar reflectors 20 arranged along the D1 direction, so that the multiple columnar reflectors 20 arranged furthest on the -D2 side are connected in a row along the D1 direction and supported by the connecting member 60.

[0024] A protrusion 67 is provided in a region NP of each of the columnar bodies 30 of the plurality of columnar reflectors 20 arranged between the plurality of columnar reflectors 20 arranged on the -D2 side in the D2 direction and aligned along the D1 direction, and the plurality of columnar reflectors 20 arranged on the +D2 side in the D2 direction and aligned along the D1 direction. When viewed from the D3 direction, the protrusion 67 is formed on the side surface 34 of the region NP of the columnar body 30 on the -D2 side of the central axis CX. The protrusion 67 protrudes from the side surface 34 of the region NP of the columnar body 30 to the -D2 side along the D2 direction. When viewed along the D2 direction, the shape of the opening of the recess 66 is the same as the shape of the protrusion 67. The recess 66 of the columnar body 30 of the columnar reflector 20 is formed so that at least the tip of the protrusion 67 of the columnar body 30 of the columnar reflector 20 adjacent to it on the +D2 side in the D2 direction can be inserted from the +D2 side along the D2 direction and can be removed to the +D2 side. The protrusion 67 of each columnar body 30 of the plurality of columnar reflectors 20 aligned along the D1 direction is inserted into the recess 66 of each columnar body 30 of the plurality of columnar reflectors 20 adjacent to it on the -D2 side, whereby the plurality of columnar reflectors 20 are connected along the D2 direction.

[0025] Although not shown, a protrusion 67 is provided and a recess 65 is formed in the region NP of each columnar body 30 of the plurality of columnar reflectors 20 arranged along the D1 direction and disposed on the +D2 side in the D2 direction. In these columnar reflectors 20, when viewed from the D3 direction, the protrusion 67 is formed in an appropriate portion on the -D2 side in the D2 direction of the central axis CX of the region NP of the columnar body 30. The recess 65 is formed on the side surface 34 on the +D2 side in the D2 direction of the central axis CX of the region NP of the columnar body 30. By inserting the plurality of protrusions 62 of the connecting member 60 into the recess 65 of each columnar body 30 of the plurality of columnar reflectors 20 arranged along the D1 direction from the +D2 side in the D2 direction, the plurality of columnar reflectors 20 arranged on the +D2 side are connected in a row along the D1 direction and supported by the connecting member 60.

[0026] For example, by inserting the protrusions 62 of the connecting member 60 into the recesses 65 and the protrusions 67 into the recesses 66, the plurality of columnar reflectors 20 are aligned in the directions D1 and D2 along the reference plane VP, and are connected to and supported by one another along the reference plane VP, as shown in Fig. 1. In the drawings other than Fig. 2 and Fig. 3, the connecting member 60, the recesses 65 and 66 of the columnar body 30, and the protrusions 67 are omitted.

[0027] Next, the principle of how an aerial image is formed by the aerial image forming element 10A and the dimensional conditions related to the aerial image forming element 10A will be described. Figures 6 and 7 are schematic diagrams for explaining the behavior of light L when it is incident on the aerial image forming element 10A. Figure 7 corresponds to an enlarged view of Figure 6 and a view of the columnar reflectors 20 cut along a plane including the D1 direction and the D3 direction, and is a schematic diagram for explaining the behavior of light L when it is incident on each columnar reflector 20 of the aerial image forming element 10A. In the following description, it is assumed that there is air outside the columnar reflectors 20, and the refractive index n １ is assumed to be 1.00, which is the same as the refractive index of air. The refractive index in this specification means the refractive index at the peak wavelength of light L.

[0028] As shown in Fig. 6, the light source S for forming the aerial image is, for example, a plurality of pixels 110 of a display 100 of a computer, mobile device, or the like capable of displaying a desired image. The light source S and the display 100 are disposed in a space on the -D3 side in the D3 direction relative to the aerial image forming element 10A. The display surface of the display 100 is inclined with respect to a reference plane VP, and moves from the -D3 side to the +D3 side in the D3 direction as it moves from the -D1 side to the +D1 side in the D1 direction. The display surface of the display 100 is flat in the D2 direction.

[0029] Although not shown, when a plurality of light sources S such as light emitting diodes (LEDs) are used instead of display 100, the plurality of light sources S are arranged along an inclined surface that moves from the −D3 side to the +D3 side as it moves from the −D1 side to the +D1 side in the D1 direction. The light emitting surface of light source S is arranged so that light L emitted from light source S travels toward aerial image forming element 10A around a virtual axis perpendicular to the inclined surface.

[0030] As shown in FIG. 6 , light L emitted from a pixel 110 passes through the pixel 110, diverges at a predetermined angle relative to a virtual axis (not shown) perpendicular to the display surface of the display 100, and is incident on one or more columnar reflectors 20 of the aerial image forming element 10A. The light L is incident on the columnar reflector 20 from the +D1 side in the D1 direction and from the -D3 side in the D3 direction. When viewed along the D2 direction, the angle of incidence of a light ray LB2, which is part of the light L emitted from the pixel 110 and travels tilted toward the -D1 side in the D1 direction relative to a light ray LB1 traveling parallel to the virtual axis, on the columnar reflector 20 is smaller than the angle of incidence of the light ray LB1 on the columnar reflector 20. The angle of incidence of a light ray LB3, which is part of the light L emitted from the pixel 110 and travels toward the +D1 side in the D1 direction relative to the light ray LB1, on the columnar reflector 20 is larger than the angle of incidence of the light ray LB1 on the columnar reflector 20.

[0031] As shown in Fig. 7, in the columnar body 30 of each columnar reflector 20, light L enters the columnar body 30 from the side surface 34p of the transmission region TF on the -D3 side of the region CF that contacts the reflective layer 50 of the adjacent columnar reflector 20 on the +D1 side in the D1 direction. The light L is refracted at the side surface 34p. If the refractive index of the transparent material that constitutes the columnar body 30 is n ２ The incident angle of the light L on the side surface 34p when viewed from the D2 direction is θ １ The refraction angle of the light L at the side surface 34p when viewed from the D2 direction is φ １ When attention is paid to the light L that passes through a plane including the D1 direction and the D2 direction, the following equation (1) is obtained according to Snell's law.

[0032]

[0033] The light L incident on the side surface 34p into the columnar body 30 reaches the side surface 34 of the reflection region RF and has a refraction angle φ with respect to the reference plane VP when viewed along the D2 direction. １ The light L is incident on the side surface 34 of the reflection region RF at the same angle as the incident light L, and is specularly reflected by the reflection layer 50. The light L specularly reflected by the reflection layer 50 reaches the side surface 34q of the transmission region TF, which is located on the +D3 side of the region CF, and is refraction at an angle φ １ The light L incident on the side surface 34q from the inside of the columnar body 30 is refracted at the side surface 34q and emitted to the outside of the columnar reflector 20.

[0034] When the light L is incident on the side surface 34p of the columnar body 30 at a steep angle, that is, when the light L is incident on the side surface 34p, the incident angle is θ １ When the angle θ is relatively larger than θ, a portion of the light L entering the interior of the columnar body 30 is incident on the side surface 34 of the reflective region RF and the end portion on the +D3 side of the reflective layer 50, is specularly reflected by the reflective layer 50, and reaches the end surface 32 instead of the side surface 34q. Another portion of the light L that is incident on the side surface 34p at a steep angle and then enters the interior of the columnar body 30 directly reaches the end surface 32. The light L that reaches the end surface 32 from the interior of the columnar body 30 is blocked by the light-shielding layer 42 and is not totally reflected at the end surface 32, and does not become stray light.

[0035] 8 corresponds to an enlarged view of FIG. 6 and a view of the columnar reflector 20 cut at the center plane in the D3 direction including the D1 and D2 directions, and is a schematic diagram for explaining the behavior of light L when it is incident on each columnar reflector 20 of the aerial image forming element 10A. As shown in FIG. 8, when viewed along the D3 direction, light L incident on the side 34p of the transmission region TF of the columnar body 30 from the +D1 side parallel to the D1 direction is refracted at the side 34p, tilted with respect to the D1 direction, and proceeds to the +D2 side of the D2 direction as it moves to the -D1 side in the D1 direction. The light L is incident at an angle θ with respect to a virtual line perpendicular to the tangent of the side 34p passing through the position where the light L is incident on the side 34p as viewed from the D3 direction. ２ The light is incident on the side surface 34p at a refraction angle φ ２ The light is incident on the interior of the columnar body 30 at .

[0036] The light L incident on the side surface 34p into the columnar body 30 reaches the side surface 34 of the reflection region RF, and when viewed along the D3 direction, the light L is refracted at an angle φ with respect to a virtual line perpendicular to the tangent to the side surface 34 that passes through the position where the light L reaches the side surface 34 of the reflection region RF. ２ The angle of incidence β according to ２ The light L is incident on the side surface 34 of the reflection region RF at a refraction angle φ with respect to a virtual line orthogonal to the tangent of the side surface 34q that passes through the position where the light L is incident on the side surface 34q when viewed from the direction D3. ２ When viewed along the D3 direction, the light L that has entered the side surface 34q from the inside of the columnar body 30 is refracted at the side surface 34q, is emitted to the outside of the columnar reflector 20, and travels parallel to the D1 direction toward the +D1 side.

[0037] As shown in FIGS. 6 to 8, light L incident on the aerial image forming element 10A is retrotransmitted through one or more columnar reflectors 20.

[0038] The light L emitted from the side surface 34q to the outside of the columnar reflector 20 has an incident angle θ with respect to the reference plane VP when viewed along the D2 direction. １The light L emitted to the outside of the columnar reflectors 20 is imaged at a position that is plane-symmetrical to the emission position of the light L in the pixels 110 of the display 100 with respect to the reference plane VP that passes through the centers of the multiple columnar reflectors 20 of the aerial image forming element 10A in the D3 direction. As a result, the light L emitted from each of the multiple pixels 110 of the display 100 forms an aerial image AR, which is a real image, by the aerial image forming element 10A at a position that is plane-symmetrical to the multiple pixels 110 of the display 100 with respect to the reference plane VP that passes through the centers of the multiple columnar reflectors 20 in the D3 direction. The observer can observe the aerial image AR in a space on the +D1 and +D3 sides of the aerial image forming element 10A, by looking down from the position that is plane-symmetrical to the multiple pixels 110 of the display 100 as described above, further on the +D1 and +D3 sides, to the -D1 and -D3 sides.

[0039] The refractive index n of the columnar body 30 ２ Regarding the above, if the body of the columnar reflector 20 is formed in a spherical shape and has a circular shape when viewed along the D2 direction and the D3 direction, the refractive index n of the transparent material of the body of the spherical reflector will be ２ is the refractive index n １ On the other hand, in the aerial image forming element 10A, the light L that enters the interior of the columnar body 30 from the side surface 34p and is irradiated onto the side surface 34 of the reflection region RF has a refraction angle φ with respect to the reference plane VP when viewed along the D2 direction. １ The shape of the inclined surface through which the light L passes inside the columnar body 30 is elliptical. Therefore, the optical path length of the light L propagating inside the columnar body 30 is longer than the optical path length of the light propagating inside the spherical body if the body of the columnar reflector 20 were formed in a spherical shape. The refraction angle φ in the columnar body 30 ２ is relatively large compared to the refraction angle at the time of retroreflection by the spherical reflector, so the refractive index n ２ is smaller than the refractive index of the spherical reflector body. １ When ２ is 2 x n １ For example, the refractive index n１ If is 1.00, the refractive index n ２ is less than 2.00.

[0040] As an example, the incident angle θ １ When an ellipsoidal lens having an elliptical inclined surface as a cross section through which light L passes inside the columnar body 30 is assumed, the focal length of the ellipsoidal lens is expressed as in equation (2) based on the lens formula.

[0041]

[0042] In formula (2), s １ represents the distance from a point corresponding to an object point on the optical axis of the incident side of the ellipsoidal lens to the lens surface, i.e., the position where the light L is incident on the elliptical inclined surface. ２ represents the distance from the lens surface to the point on the optical axis corresponding to the image point. a represents the half value of the major axis of the elliptical inclined surface. b represents the half value of the diameter of the columnar body 30, which is equal to the radius r.

[0043] Equation (3) holds true for the cross section of the ellipsoidal lens, that is, the long and short sides of the elliptical inclined surface.

[0044]

[0045] Based on the formulas (1) to (3), the refractive index n ２ Regarding this, the following equation (4) is obtained.

[0046]

[0047] The angle that the end face 31 of the columnar body 30 makes with respect to the reference plane VP is defined as α. The angle that the end face 32 of the columnar body 30 makes with respect to the reference plane VP is defined as the same as the angle that the end face 31 makes with respect to the reference plane VP. The angle that the end face 32 of the columnar body 30 makes with respect to the reference plane VP is defined as α. A ray LBx of light L enters the interior of the columnar body 30 from the side surface 34p on the +D3 side in the D3 direction so as not to be blocked by the columnar body 30 and reflective layer 50 of the adjacent columnar reflector 20 on the +D3 side in the D1 direction. When the light ray LBx is specularly reflected at the end of the side surface 34 of the reflection region RF and the reflective layer 50 on the -D1 side in the D1 direction and the +D3 side in the D3 direction, the following formula (5) holds.

[0048]

[0049] For example, the diameter d of the columnar body 30 is set to 1.0 mm, and the refractive index n ２ If is set to 1.71, the following equations (6) and (7) are obtained from equations (1) and (5).

[0050]

[0051] The angle α of the end faces 31 and 32 of the columnar body 30 relative to the reference plane VP is the refraction angle φ of the light L. １ The above is true, and the incident angle θ of the light L １ Therefore, the following equation (8) holds true.

[0052]

[0053] Although not shown, the angle α is the refraction angle φ １ If the angle α is smaller than the incident angle θ, the height of the side surface 34p at which the light L can enter the interior of the columnar body 30, i.e., the size in the D3 direction, decreases, the amount of light L taken into the columnar reflector 20 decreases, and the aerial image AR becomes dark. １ If the angle α is larger than the incident angle θ, a part of the light L including the light ray LBx is blocked by the columnar reflector 20 adjacent to the columnar body 30 of the columnar reflector 20 on the +D1 side in the D1 direction, and a part of the light L does not reach the side surface 34 of the reflection region RF and the reflection layer 50, reducing the amount of light L emitted from the columnar reflector 20 and darkening the aerial image AR.１ If it is larger than , another part of the light L reaches the end surface 31 and is lost, and does not contribute to the formation of the aerial image AR.

[0054] Incident angle θ of light L １ is 45°, and the angle that the viewer's line of sight makes with respect to the reference plane VP when observing the aerial image AR is approximately 45°, the angle α can be calculated from equation (6) as shown in the following equation (9).

[0055]

[0056] The maximum height h2 of the side surface 34 means the height h2 in the D3 direction of the end closest to the +D1 side in the D1 direction of the side surface 34 of the columnar body 30. The minimum height h1 of the side surface 34 means the height h1 in the D3 direction of the end closest to the −D1 side in the D1 direction of the side surface 34. The height h2 of the side surface 34 is calculated using the height h1 of the side surface 34, the diameter d of the columnar body 30, and the angle α between the end faces 31, 32, as shown in the following formula (10).

[0057]

[0058] The incident angle θ of the light L to the columnar body 30 １ is 45°, and the refractive index n １ is 1.00, and the refractive index n ２ When the refractive index is 1.71, the refraction angle φ of the light L in the columnar body 30 calculated by the formula (6) is １ is 24.4°. In this case, for example, when the diameter d of the columnar body 30 is 1.0 mm, the minimum height of the columnar body 30 in the D3 direction, i.e., the minimum height h1 of the side surface 34, calculated by equation (7) is 0.454 mm. For example, when the angle α of the end faces 31, 32 of the columnar body 30 is 30.0°, the maximum height of the columnar body 30 in the D3 direction, i.e., the maximum height h2 of the side surface 34, is 1.61 mm from equations (10) and (11) shown below.

[0059]

[0060] The diameter d of the columnar body 30 is related to the resolution of the aerial image AR. Basically, the smaller the diameter d of the columnar body 30, the higher the resolution of the aerial image AR. In the aerial image forming element 10A, the incident angle θ of the light L is determined taking into consideration, for example, the original image of the aerial image AR displayed by the light source S and the plurality of pixels 110 of the display 100, the size of the formed aerial image AR, and the relative position of the aerial image AR with respect to the viewer. １ is set appropriately. The incident angle θ １ By setting the refractive index n of the outside of the columnar reflector 20, the arrangement and posture of the light source S and the display 100 relative to the aerial image forming element 10A are appropriately set as shown in FIG. １ , and the refractive index n of the columnar body 30 ２ When is appropriately set, the refraction angle φ of the light L in the columnar body 30 １ is calculated, and the allowable range of the angle α between the end faces 31, 32 is determined. When the diameter d of the columnar body 30 is appropriately set in consideration of the resolution of the aerial image AR, the minimum height h1 of the side face 34 is calculated. When the angle α between the end faces 31, 32 is appropriately set within the allowable range of the angle α, the maximum height h2 of the side face 34 is calculated, and the shape and size of the columnar body 30 are determined.

[0061] The number of columnar reflectors 20 provided in the aerial image forming element 10A is determined according to the incident area of ​​light L emitted from the light source S and the multiple pixels 110 of the display 100 and spreading within a reference plane VP including the end of the aerial image forming element 10A on the -D3 side in the D3 direction, and is appropriately set so that the area occupied by the multiple columnar reflectors 20 on the reference plane VP includes the incident area of ​​light L.

[0062] A ray LBy of light L enters the columnar body 30 of one columnar reflector 20 from the side surface 34p that is furthest to the -D3 side in the D3 direction. The ray LBy is specularly reflected by the end of the side surface 34 of the reflection region RF and the reflection layer 50 that is furthest to the -D1 side in the D1 direction and furthest to the -D3 side in the D3 direction, and reaches the side surface 34q. The ray LBy is refracted by the end of the side surface 34q that is furthest to the +D1 side in the D1 direction and furthest to the -D3 side in the D3 direction, and is emitted to the outside of the columnar reflector 20, contributing to the formation of the aerial image AR.

[0063] The region NP in the columnar body 30 through which the light L does not pass is a region between the light rays LBx and LBy of the light L propagating in the columnar body 30 between the side surface 34p and the side surface 34 of the reflection region RF in the D3 direction. When viewed along the D2 direction, the region NP is spaced apart from the center of the columnar body 30 on the central axis CX in the D1 and D3 directions by 2×φ １ When viewed along the D3 direction, the region NP is a region on the +D1 side in the D1 direction of the positions RP1 and RP2 of the side surface 34. In other words, when viewed along the D3 direction, the region NP through which the light L does not pass is a region from the position RP1 in the circumferential direction around the central axis CX within the reference plane VP, to the position RP1 when the height of the side surface 34 in the D3 direction is moved counterclockwise in FIG. 8, that is, to the position RP1 when the height of the side surface 34 in the D3 direction is increased once and then decreased.

[0064] In the region NP of the columnar body 30 where light L does not pass, components for connecting two or more columnar reflectors 20 adjacent to each other on the reference plane VP are formed. The components for connecting two or more columnar reflectors 20 may include the protrusions and recesses exemplified in the above description, but components other than the protrusions and recesses may also be provided. For example, recesses may extend in the D2 direction and penetrate the columnar body 30 along the D2 direction. A large portion of the region NP of the columnar body 30 where light L does not pass may be removed. The fact that the cross-sectional shape of the columnar body 30 including the D1 and D3 directions is a trapezoid narrowing toward the -D1 side in the D1 direction means that when moving from the +D1 side to the -D1 side in the D1 direction, the end face 31 moves to the +D3 side in the D3 direction, while the end face 32 moves to the -D3 side in the D3 direction, reducing the distance in the D3 direction between the end face 31 and the end face 32, and the height of the side face 34 is smallest at the end on the -D1 side in the D1 direction. As described above, a configuration in which most of the region NP in the columnar body 30 through which light L does not pass has been removed, and a configuration in which another component or material is placed in the portion from which most of the region NP has been removed, are included in configurations in which the cross-sectional shape of the columnar body 30 including the D1 direction and the D3 direction is a trapezoid that narrows toward the -D1 side of the D1 direction.

[0065] The aerial image forming element 10A of the present embodiment described above includes a plurality of columnar reflectors 20 arranged along a reference plane VP including a D1 direction (first direction) and a D2 direction (second direction) perpendicular to the D1 direction. Each columnar reflector 20 includes a columnar body 30, a light-shielding layer (first light-shielding layer) 41, a light-shielding layer (second light-shielding layer) 42, and a reflective layer 50. The columnar body 30 has a central axis CX parallel to a D3 direction (third direction) perpendicular to the reference plane VP. The columnar body 30 includes an end face (first end face) 31 on the −D3 side (first side) in the D3 direction, an end face (second end face) 32 on the +D3 side (second side) opposite the −D3 side in the D3 direction, and a side surface 34 connecting the end face 31 and the end face 32 along the D3 direction. The columnar body 30 is made of a transparent material that is transparent to incident light L. The cross section of the columnar body 30 taken along the D1 and D3 directions has a trapezoidal shape that narrows toward the −D1 side (first side) in the D1 direction. The light-shielding layer 41 is provided on the end face 31 of the columnar body 30 and blocks light incident on the end face 31 from outside the columnar body 30. The light-shielding layer 42 is provided on the end face 32 of the columnar body 30. The light-shielding layer 42 blocks light incident on the end face 32 from outside the columnar body 30 and blocks light incident on the end face 32 from inside the columnar body 30, thereby eliminating stray light. The reflective layer 50 is provided in a reflective region RF of the side face 34 of the columnar body 30 and reflects light L propagating inside the columnar body 30. The reflective region RF is a region of the side face 34 on the −D1 side in the D1 direction of positions RP1 and RP2 that are identical to the central axis CX.

[0066] In the aerial image forming element 10A of this embodiment, light L emitted from the light source S is incident on the multiple columnar reflectors 20 from the -D3 side in the D3 direction and the +D1 side in the D1 direction. The light L enters the interior of the columnar body 30 from the side surface 34p of the transmission region TF where the reflective layer 50 is not provided in each columnar body 30 of the multiple columnar reflectors 20, is specularly reflected by the reflective layer 50, and is emitted from the side surface 34q of the transmission region TF of the columnar body 30 to an area on the +D3 side in the D3 direction and the +D1 side in the D1 direction relative to the multiple columnar reflectors 20. The light L retrotransmits through the multiple columnar reflectors 20 and forms an aerial image AR at a position symmetrical to the light source S with respect to a reference plane VP passing through the centers of the multiple columnar reflectors 20 in the D3 direction. Since the light-shielding layers 41, 42 are provided on the end faces 31, 32 of the columnar body 30, light that does not contribute to the aerial image AR, such as stray light from multiple columnar reflectors 20, is suppressed as much as possible, and the visibility of the aerial image AR is high.

[0067] In the aerial image forming element 10A of this embodiment, the end faces 31, 32 of the columnar bodies 30 of the multiple columnar reflectors 20 are inclined with respect to the reference plane VP. As the end face 31 moves from the +D1 side to the -D1 side in the D1 direction, it moves toward the +D3 side in the D3 direction. As the end face 32 moves from the +D1 side to the -D1 side in the D1 direction, it moves toward the opposite side of the end face 31 in the D3 direction, i.e., the end faces 31, 32 move toward the +D3 side in the D2 direction. Figure 9 is a perspective view of the aerial image forming element 10A of this embodiment, as seen from a direction along the viewer's line of sight. 9, in the configuration of the aerial image forming element 10A of this embodiment, for an observer directing their gaze toward the -D1 side along the D1 direction and the -D3 side in the D3 direction, light L emitted from the side surface 34q of the transmission region TF in the columnar body 30 of the plurality of columnar reflectors 20 passes through the end surfaces 32 of the columnar body 30 of the plurality of columnar reflectors 20 that contact them on the +D1 side in the D1 direction and the +D3 side in the D3 direction of the light-shielding layer 42, and forms an aerial image AR without being blocked by the plurality of columnar reflectors 20, and reaches the observer's eyes. According to the aerial image forming element 10A of this embodiment, the amount of light of the aerial image AR that reaches the observer's eyes is increased.

[0068] In the aerial image forming element 10A of this embodiment, two or more of the plurality of columnar reflectors 20 are in contact with each other without any gap in the D1 direction and the D2 direction. However, two or more of the plurality of columnar reflectors 20 may be appropriately spaced apart at a predetermined interval in the D1 direction and the D2 direction. "Two or more columnar reflectors 20 are spaced apart at a predetermined interval" means that the distance between adjacent columnar reflectors 20 in the D1 direction and the D2 direction is a distance that allows the formation of an aerial image AR with the desired resolution, and is at least smaller than the distance between cylindrical columnar bodies whose end faces on the light output side are parallel to a plane corresponding to the reference plane, as in the optical plate (aerial image forming element) disclosed in Patent Document 1.

[0069] For example, in the optical plate (aerial image forming element) disclosed in Patent Document 1, multiple cylinders are arranged at intervals along the surface of a mirror corresponding to the reference plane VP. Figure 10 is a perspective view of the optical plate disclosed in Patent Document 1, as viewed from a direction along the line of sight of the observer. As shown in Figure 10, in the optical plate disclosed in Patent Document 1, in order to form an aerial image and deliver it to the observer's eye without blocking the light L emitted from the multiple cylinders by the multiple cylinders arranged on the +D1 side of the D1 direction, the multiple cylinders must be arranged at sufficient intervals along the surface corresponding to the reference plane VP.

[0070] On the other hand, in the aerial image forming element 10A of this embodiment, two or more columnar reflectors 20 are in contact with each other within a reference plane VP including the D1 and D2 directions, or are appropriately spaced apart, so compared to conventional aerial image forming elements, the columnar reflectors 20, which are the smallest unit configurations for emitting light L, are densely arranged on the reference plane VP. As shown in FIG. 9, in the aerial image forming element 10A of this embodiment, the end faces 32 of the columnar bodies 30 of each columnar reflector 20 descend to the -D3 side as they move toward the -D1 side. Therefore, even if multiple columnar reflectors 20 are densely arranged within the reference plane VP, in the observation direction of the aerial image AR, that is, in the direction looking down on the aerial image forming element 10A from the +D1 side and +D3 side of the aerial image forming element 10A in the vertical direction, the side surfaces 34q of the columnar bodies 30 of each columnar reflector 20 are exposed without being obstructed by the columnar reflectors 20 adjacent to the +D1 side of each columnar reflector 20. Even if multiple columnar reflectors 20 are densely packed within the reference plane VP as described above, an aerial image AR (not shown) is formed by light L emitted from the side surfaces 34q of the columnar bodies 30 of the multiple columnar reflectors 20, and the light L reaches the observer's eyes. In the aerial image forming element 10A of this embodiment, the distance between two adjacent columnar reflectors 20 is smaller than in conventional aerial image forming elements. The aerial image forming element 10A of this embodiment can increase the resolution of the aerial image AR.

[0071] As the distance between two or more of the plurality of columnar reflectors 20 in the D1 direction and the D2 direction increases, the viewing angle of the aerial image AR in the horizontal direction, i.e., the direction parallel to the reference plane VP, increases, but the resolution of the aerial image AR when viewed from the front along the D1 direction decreases. The viewing angle of the aerial image AR in the horizontal direction and the resolution when viewed from the front depend on the distance between the two or more columnar reflectors 20 in the D1 direction and the D2 direction, and are in a trade-off relationship with each other. When the distance between the two or more columnar reflectors 20 in the D1 direction and the D2 direction is within the above-mentioned appropriate range and the resolution of the aerial image AR is within an acceptable range, the viewing angle of the aerial image AR in the horizontal direction can be suitably adjusted by adjusting the distance between the two or more columnar reflectors 20 in the D1 direction and the D2 direction. For example, if the diameter of the columnar body 30 is 1.0 mm and the spacing between two or more columnar reflectors 20 in the D1 and D2 directions is 0.2 mm, the aerial image AR can be observed from an angle of 70° in the horizontal direction, i.e., in the D2 direction within a plane parallel to the reference plane VP, centered on the D1 direction from the +D1 side to the -D1 side, which is the observation direction of the aerial image AR, and the viewing angle can potentially be expanded to approximately 140°.

[0072] In the optical plate disclosed in Patent Document 1, the area of ​​the end faces of the multiple cylinders on the +D3 side in the D3 direction and the light-shielding layer occupying within the viewer's field of view is relatively large. On the other hand, as shown in Figure 9, in the aerial image forming element 10A of this embodiment, the end faces 32 of the columnar bodies 30 of the multiple columnar reflectors 20 and the light-shielding layer 42 move toward the -D3 side in the D3 direction as they move toward the -D1 side in the D1 direction, similar to the viewer's line of sight, so the area of ​​the light-shielding layer 42 occupying within the viewer's field of view can be reduced. The aerial image forming element 10A of this embodiment can further improve the visibility of the aerial image AR.

[0073] In the aerial image forming element 10A of this embodiment, two or more of the plurality of columnar reflectors 20 are in contact with each other without any gap in the D1 direction.

[0074] According to the aerial image forming element 10A of this embodiment, the distance between two adjacent columnar reflectors 20 in the D1 direction is zero, so that the resolution of the aerial image AR can be maximized when viewed from the front along the D1 direction.

[0075] In the aerial image forming element 10A of this embodiment, two or more of the plurality of columnar reflectors 20 may be arranged at a predetermined interval from each other in the D1 direction.

[0076] According to the above-described aerial image forming element, the distance between two adjacent columnar reflectors 20 in the D1 direction is sufficiently smaller than that of conventional aerial image forming elements, and therefore the resolution of the aerial image AR can be improved when viewed from the front along the D1 direction compared to conventional aerial image forming elements. With the above-described aerial image forming element, the number of columnar reflectors 20 in the D1 direction can be reduced compared to when two or more columnar reflectors 20 are in contact with each other without any distance between them in the D1 direction.

[0077] In the aerial image forming element 10A of this embodiment, two or more of the plurality of columnar reflectors 20 are in contact with each other without any gap in the D2 direction.

[0078] According to the aerial image forming element 10A of this embodiment, the distance between two adjacent columnar reflectors 20 in the D2 direction is zero, so that the resolution of the aerial image AR can be maximized when observed from a direction horizontally shifted from the D1 direction, i.e., from a direction shifted by an angle within the range of the field of view within a plane parallel to the reference plane VP.

[0079] When two or more of the multiple columnar reflectors 20 are in contact with each other without any spacing in both the D1 direction and the D2 direction, as in the aerial image forming element 10A of this embodiment, the resolution of the aerial image AR can be further improved throughout the entire range of the field of view compared to a configuration in which two or more columnar reflectors 20 are arranged with spacing between them in the D1 direction and the D2 direction.

[0080] In the aerial image forming element 10A of this embodiment, two or more of the plurality of columnar reflectors 20 may be arranged at a predetermined interval from each other in the D2 direction.

[0081] According to the above-described aerial image forming element, the distance between two adjacent columnar reflectors 20 in the D2 direction is sufficiently smaller than that of conventional aerial image forming elements, so that when observed from a direction shifted by an angle within the range of the field of view from the D1 direction in a plane parallel to the reference plane VP, the resolution of the aerial image AR can be improved compared to that of conventional aerial image forming elements. With the above-described aerial image forming element, the number of columnar reflectors 20 in the D2 direction can be reduced compared to when two or more columnar reflectors 20 are in contact with each other in the D2 direction without any distance therebetween.

[0082] In the aerial image forming element 10A of this embodiment, the cross section of the columnar body 30 including the D1 direction and the D2 direction has a circular shape.

[0083] According to the aerial image forming element 10A of this embodiment, when viewed along the D3 direction, the light L incident on each columnar body 30 of the multiple columnar reflectors 20 can be effectively retroreflected, the amount of light L that retrotransmits through the multiple columnar reflectors 20 to form the aerial image AR can be increased, and stray light and light that is actually lost can be minimized.

[0084] As described above, when the cross section of the columnar body 30 including the D1 direction and the D2 direction has a circular shape, the accuracy with which the light L incident on the columnar body 30 is retroreflected increases. As long as the light L incident on the columnar body 30 is retroreflected to an extent that the brightness and visibility of the aerial image AR can be ensured, the cross section of the columnar body 30 including the D1 direction and the D2 direction may have a shape other than a circle. The shape other than a circle is determined, for example, by the diameter d of the columnar body 30, i.e., the maximum diameter in the D1 direction and the D2 direction, and examples of shapes other than a circle include a regular polygon with 12 or more corners.

[0085] In the aerial image forming element 10A of this embodiment, the angles that the first end face and the second end face make with respect to the reference plane are expressed by the following equation (12).

[0086]

[0087] In formula (12), α represents the angle formed by the end face (first end face) 31 and the end face (second end face) 32 of the columnar body 30 with respect to the reference plane VP. １represents the refractive index outside the plurality of columnar reflectors 20. ２ represents the refractive index of the transparent material that constitutes the columnar body 30. １ represents the angle of incidence of light L incident on the side surface 34p of the columnar body 30, and means the angle that the center line of the viewer's line of sight when viewing the aerial image AR makes with respect to the reference plane VP.

[0088] In the aerial image forming element 10A of this embodiment, by setting the angle α within the range of the condition expressed by equation (12), the amount of light L emitted from the multiple columnar reflectors 20 to form the aerial image AR can be increased, thereby improving the brightness and visibility of the aerial image AR. If the angle α is smaller than the lower limit of equation (12), the side surface 34p onto which the light L is incident on each columnar body 30 of the multiple columnar reflectors 20 becomes excessively small, thereby reducing the amount of light L forming the aerial image AR. On the other hand, if the angle α is larger than the upper limit of equation (12), a portion of the light L incident toward the side surface 34p of each columnar body 30 of the multiple columnar reflectors 20 is blocked by the columnar body 30 of the columnar reflector 20 adjacent to the +D1 side in the D1 direction, and a portion of the light L cannot enter the interior of each columnar body 30. If the angle α is larger than the upper limit value of formula (12), another part of the light L that enters the interior of the columnar body 30 from the side surface 34p of the columnar body 30 enters the end surface 31 and is lost by the light-shielding layer 41. In other words, if the angle α is larger than the upper limit value of formula (12), the amount of light L that forms the aerial image AR decreases.

[0089] [Evaluation Example Using Optical Simulation] Next, the results of an evaluation of the aerial image forming element 10A of this embodiment using optical simulation will be described. In this evaluation example, the aerial image forming element 10A was used as an example, and an aerial image forming element in which multiple cylindrical reflectors were arranged at intervals along the D1 and D2 directions as illustrated in FIG. 10 was used as a comparative example. The aerial image forming elements of the example and comparative example were modeled in Blender, and a simulation of the aerial image was performed using Cycles as the rendering engine. The cylindrical reflector of the comparative aerial image forming element has the same configuration as the columnar reflector 20 in the aerial image forming element 10A, except that the end face in the D3 direction is parallel to the reference plane VP, the D1 direction, and the D2 direction. The present invention is not limited to the content of the evaluation example described below.

[0090] In this evaluation example, distance 1 in Blender was assumed to be 1 cm in real space as a unit of distance. In modeling within Blender, the reflectivity of the columnar reflector 20 and the reflective layer 50 of the columnar reflector was set to 0.87. Refraction BSDF was used for the transmitting surface of the columnar body 30, i.e., the exposed side surface 34, and the refractive index of the columnar body 30 was set to 1.71. The diameter of the columnar body 30 was set to 1.00 mm. For the aerial image forming element 10A of the example, the minimum height h1 in the D3 direction of the columnar body 30 and the reflective layer 50 was set to 0.455 mm, and the angle α of the end faces 31 and 32 relative to the reference plane VP was set to 35°. For the aerial image forming element of the comparative example, the height in the D3 direction was set to 1.37 mm, which corresponded to three times the height h1 in the D3 direction of the columnar body 30 and the reflective layer 50 in the aerial image forming element 10A of the example. For the aerial image forming element of the comparative example, the spacing between the cylindrical reflectors in the D1 and D2 directions was set to 0.455 mm, which corresponded to the height h1 of the columnar body 30 and the reflective layer 50 in the aerial image forming element 10A of the example.

[0091] FIG. 11 shows an aerial image AR obtained by rendering the aerial image forming element 10A of the example based on the above settings. FIG. 12 shows an aerial image obtained by rendering the aerial image forming element of the comparative example based on the above settings. As shown in FIGS. 11 and 12, the aerial image AR formed by the aerial image forming element 10A of the example is brighter than the aerial image formed by the aerial image forming element of the comparative example. In the aerial image AR formed by the aerial image forming element 10A of the example, the outline of the katakana character "i" is clearer than in the aerial image formed by the aerial image forming element of the comparative example. From these findings, the aerial image AR formed by the aerial image forming element 10A of the example had a higher resolution than the aerial image formed by the aerial image forming element of the comparative example.

[0092] From the results of the optical simulation described above, it was confirmed that the aerial image forming element 10A of the embodiment improves the resolution of the aerial image AR, increases the amount of light of the aerial image AR that reaches the observer's eyes, and forms a bright aerial image AR.

[0093] Although the preferred embodiments of the present invention have been described in detail above, the present invention is not limited to the specific embodiments, and various modifications and variations can be made within the scope of the gist of the present invention as defined in the claims.

[0094] In the aerial image forming element 10A of the above-described embodiment, when viewed along the D3 direction, the plurality of columnar reflectors 20 are aligned in two directions, the D1 direction and the D2 direction, within the reference plane VP. The plurality of columnar reflectors 20 are two-dimensionally arranged in the D1 direction and the D2 direction. Two or more of the plurality of columnar reflectors 20 are arranged at the same position in the D1 direction and aligned along the D1 direction. For each of the two or more columnar reflectors 20 aligned at the same position in the D1 direction, two or more columnar reflectors 20 are aligned at the same position in the D2 direction and aligned along the D2 direction. FIG. 13 is a plan view of an aerial image forming element 10B, which is a modified example of the aerial image forming element 10A. As shown in FIG. 13, in the aerial image forming element 10B, when viewed along the D3 direction, two or more of the plurality of columnar reflectors 20 are adjacent to each other in the D1 direction, aligned at the same position, and aligned along the D1 direction. Two or more other columnar reflectors 20 among the plurality of columnar reflectors 20 are arranged at positions different from each other in the D2 direction. That is, the plurality of columnar reflectors 20 may be arranged in a so-called staggered manner in the D2 direction.

[0095] In the aerial image forming element of the present invention, the mechanism for supporting or fixing the plurality of columnar reflectors along the reference plane is not limited to the configuration exemplified in the above-mentioned embodiment. For example, the plurality of columnar reflectors may be inserted into a plurality of through holes formed along the third direction in a substrate having a plate surface parallel to the reference plane. The light-blocking regions NP in the columnar bodies of the plurality of columnar reflectors may be directly connected to each other or may be connected via a separate connecting member.

[0096] 10A, 10B Aerial image forming element 20 Columnar reflector 30 Column body 31 End face (first end face) 32 End face (second end face) 34 Side surface 41 Light shielding layer (first light shielding layer) 42 Light shielding layer (second light shielding layer) 50 Reflective layer D1 direction (first direction) D2 direction (second direction) D3 Direction (3rd direction) VP Reference plane

Claims

1. A method for manufacturing a light-emitting diode (LED) comprising: providing a plurality of columnar reflectors arranged along a reference plane including a first direction and a second direction perpendicular to the first direction; the columnar reflectors each having a central axis parallel to a third direction perpendicular to the reference plane, the columnar reflectors each having a first end face on a first side in the third direction, a second end face on a second side opposite to the first side in the third direction, and a side surface connecting the first end face and the second end face along the third direction, the columnar reflectors each having a transparent material transparent to incident light; a first light-shielding layer provided on the first end face for blocking light from outside the columnar body; a second light-shielding layer provided on the second end face for blocking light from outside the columnar body; and a reflective layer provided in a reflective region of the side surface for reflecting light propagating inside the columnar body; and the shape of a cross section of the columnar body including the first direction and the third direction is a trapezoid narrowing toward the first side in the first direction, an aerial image forming element, wherein the reflective region is a region on the side surface on a first side in the first direction from a position on the side surface that is the same as the central axis in the first direction when viewed from the third direction.

2. The aerial image forming element according to claim 1, wherein two or more of the plurality of columnar reflectors are in contact with each other without any gap in between in the first direction.

3. The aerial image forming element according to claim 1, wherein two or more of the plurality of columnar reflectors are arranged at a predetermined interval from each other in the first direction.

4. An aerial image forming element as described in claim 1 or claim 2, wherein two or more of the multiple columnar reflectors are in contact with each other without any gap in the second direction.

5. An aerial image forming element described in any one of claims 1 to 3, wherein two or more of the plurality of columnar reflectors are arranged at a predetermined interval from each other in the second direction.

6. An aerial image forming element as described in any one of claims 1 to 3, wherein the cross-sectional shape of the columnar body including the first direction and the second direction is circular.

7. An aerial image forming element as described in any one of claims 1 to 3, wherein the angles that the first end face and the second end face make with respect to the reference plane are expressed by the following equation (1). In formula (1), α is the angle that the first end surface and the second end surface make with respect to the reference plane, and n １ The refractive index of the exterior of the plurality of columnar reflectors is n ２ the refractive index θ of the transparent material; １ is the angle of incidence of light incident on the side surface of the columnar body.

Images