WO2012046296A1 - Spatial image display device - Google Patents

Abstract

Provided is a spatial image display device comprising an optically reflective element that reflects display light from a real object region to an observer. A first assembly and a second assembly comprise a plurality of longitudinal members which have each an optically reflective face in the longitudinal direction, and in each assembly the plurality of longitudinal members are arranged such that the optically reflective faces thereof are oriented in the same direction. The optically reflective element is formed by superimposing the first assembly and the second assembly in such a way that the optically reflective faces of the first assembly and the second assembly are orthogonal to each other. The light from the real object region is reflected once by each of the optically reflective faces of the first assembly and the second assembly and thereby forms a real image. When the optically reflective faces of the first assembly are arranged at an inclination from the back left towards the front right as seen from the viewing direction of the observer, and the optically reflective faces of the second assembly are arranged at an inclination from the back right towards the front left as seen from the viewing direction of the observer, the thickness of the first assembly decreases from the left-hand direction towards the right-hand direction as seen from the viewing direction of the observer, and the thickness of the second assembly decreases from the right-hand direction towards the left-hand direction as seen from the viewing direction of the observer.

Description

Spatial image display device

The present invention relates to a spatial video display device that displays video in a space.

Conventionally, various optical elements have been developed to realize realistic 3D aerial images. For example, in Patent Document 1, an image of an object, which is a projection object placed on one side of an element, is formed on a position that is a surface object on the opposite side of the element by using a reflection-type plane-symmetric imaging element. A spatial video display device is disclosed. The reflection-type plane-symmetric imaging element used in this spatial image display device has a plurality of holes that penetrate a predetermined base in the thickness direction, and is a unit optical system that is composed of two mirror surface elements orthogonal to the inner wall of each hole An element is formed, and when light is transmitted from one surface direction of the substrate to the other surface direction through the hole, the light is reflected once by each of the two mirror elements. The light emitted from the projection is reflected by one of the two mirror elements when passing through the unit optical element of the reflective surface-symmetric imaging element, and then reflected by the mirror surface to become reflected light. The light is reflected by the other of the two specular elements of the unit optical element, and the projection object is imaged at a position reflected on the virtual mirror.

However, since the optical element described above requires a very fine processing technique, there is a problem in that a spatial image display device using such an optical element is expensive to manufacture. In view of this, the present applicant has proposed a reflection-type plane-symmetric imaging element that does not require manufacturing costs in Patent Document 2.

FIGS. 1 to 3 are diagrams showing the configuration of a reflection-type plane-symmetric imaging element (hereinafter referred to as a light reflection optical element) proposed in Patent Document 2. FIG. FIG. 1 is an external view of a light reflecting optical element, FIG. 2 is an external view of a rectangular parallelepiped material constituting the light reflecting optical element, and FIG. 3 is an external view showing a combination of two mirror sheets forming the light reflecting optical element.

As shown in FIGS. 1 and 3, the light reflecting optical element 2 has two mirror sheets 21 and 22 each formed by closely contacting a large number of rod-shaped rectangular parallelepiped materials 20 in parallel.

As shown in FIG. 2, the rectangular parallelepiped material 20 is a long member, and is represented by transparent acrylic whose one side of a rectangular cross section in the direction perpendicular to the longitudinal direction, that is, in the short direction, is several hundred μm to several cm. Made of plastic or glass rod. The length varies depending on the size of the image to be projected, but is about several tens mm to several m. Note that three of the four surfaces extending in the longitudinal direction are surfaces used for light transmission or reflection, and thus are in a smooth state. About 100 to 20000 rectangular parallelepiped materials 20 are used for each of the mirror sheets 21 and 22.

As shown in FIG. 2, a light reflecting film 23 is formed on one surface of the rectangular parallelepiped material 20 extending in the longitudinal direction, thereby forming a light reflecting surface. The light reflecting film 23 is formed by vapor deposition or sputtering of aluminum or silver.

With respect to such a plurality of rectangular parallelepiped members 20, a mirror sheet 21 is formed by bringing the opposite surface 24 opposite to the surface on which the light reflecting film 23 of one rectangular parallelepiped member 20 is formed into close contact with the light reflecting surface 23 of another rectangular parallelepiped member 20. , 22 are formed. As shown in FIG. 3, the mirror sheets 21 and 22 are bonded together in a state in which one of the rectangular parallelepiped materials 20 is rotated by 90 degrees so that the parallel directions of the rectangular parallelepiped materials 20 intersect, thereby forming the light reflecting optical element 2. Is done. A portion where each rectangular parallelepiped material 20 of the mirror sheet 21 and each rectangular parallelepiped material 20 of the mirror sheet 22 intersect constitutes a minute mirror unit (unit optical element), and the light reflecting surface 23 of the mirror sheet 21 of each minute mirror unit is the first. The light reflecting surface 23 of the mirror sheet 22 becomes the second light reflecting surface.

In the spatial image display device using the light reflecting optical element 2, as shown in FIG. 4, the object 1 is disposed on one surface side of the light reflecting optical element 2, and the light reflecting optical element 2 includes the object 1 from the object 1. Light is incident obliquely. The observer's eyes E are positioned on the other surface side of the light reflecting optical element 2, and a real image 3, that is, a spatial image is formed at a spatial position that is plane-symmetric with the object 1 with respect to the light reflecting optical element 2. Note that the lower end A and the upper end A ′, which are both ends of the light reflecting optical element 2 in FIG. 4, correspond to the opposing angles A and A ′ of the light reflecting optical element 2 in FIG. 1. More specifically, as shown in FIG. 5, the light from the object 1 is reflected on the light reflecting surface 23 (second light reflecting surface) of the mirror sheet 22 in the direction of the arrow Y1, and the reflected light is reflected in the direction of the arrow Y2. Since the light is reflected on the light reflecting surface 23 (first light reflecting surface) of the mirror sheet 21 and the reflected light travels toward the observer in the direction of the arrow Y3, each light reflecting surface 23 of the light reflecting optical element 2 has 1 each. It is designed to create a mirror image by reflecting twice, that is, twice.

JP 2008-158114 A International Publication No. WO2009 / 136578 Pamphlet

However, in the spatial video display device disclosed in Patent Document 2, when the line of sight is shifted from the design line-of-sight direction to the left-right direction (the left-right direction illustrated in FIG. 1; the direction perpendicular to the paper surface in FIG. 4), 22, the light that is transmitted without being reflected and the light that is reflected twice or more are increased, that is, the light that is reflected only once is reduced in each of the mirror sheets 21 and 22. However, there is a problem that the brightness of the spatial image varies depending on the left-right direction.

The present invention has been made in view of the above circumstances, and an example of the problem is a spatial video display that can ensure the brightness of a spatial video even if the line of sight is shifted from the design line of sight to the horizontal direction. To provide an apparatus.

In order to achieve the above object, one aspect of the present invention is a spatial image display device including a light reflecting optical element that reflects light from a substantial part toward an observer, and the light reflecting optical element includes: The first assembly and the second assembly in which a plurality of longitudinal members having one light reflecting surface are arranged so that the light reflecting surfaces are in the same direction are overlapped so that the light reflecting surfaces are orthogonal to each other. Each of the plurality of longitudinal members constituting the first assembly and the second assembly is composed of a translucent rectangular parallelepiped having four surfaces extending in the longitudinal direction, and one of the four surfaces is The light reflecting surface, and in each of the first aggregate and the second aggregate, the light reflecting surface of one rectangular parallelepiped and the surface facing the light reflecting surface of the adjacent rectangular parallelepiped are in contact with each other. The rectangular parallelepiped is arranged to receive light from the entity part. Each of the first aggregate and the second light aggregate is reflected once on the light reflecting surface to form a real image, and the light reflecting surface of the first aggregate is moved from the line of sight of the observer. The light reflecting surfaces of the second assembly are obliquely arranged from the left back direction to the right front direction as viewed from the left, and the light reflecting surface of the second aggregate is directed from the right back direction to the left front direction as viewed from the line of sight of the observer. The thickness of the first assembly, which is the length of the light reflecting surface of the first assembly in the short direction, is the left direction when viewed from the observer's line of sight And the thickness of the second aggregate, which is the length in the short direction of the light reflecting surface of the second aggregate, is the direction of the line of sight of the observer. It is formed so as to become thinner from the right direction to the left direction when viewed from the side.

It is an external view of a light reflection optical element. It is an external view of the rectangular parallelepiped material which comprises the light reflection optical element of FIG. It is a figure which shows the combination of two mirror sheets which form the light reflection optical element of FIG. It is the schematic of the optical system of the spatial image display apparatus using the light reflection optical element of FIG. It is a schematic diagram which shows a mode that light reflects twice in the light reflection optical element of FIG. 1 is an external perspective view of a light reflecting optical element according to an embodiment of the present invention. It is an external appearance perspective view of the 1st mirror sheet which comprises the light reflection optical element of FIG. FIG. 7 is a top view, a side view, and a front view of a first mirror sheet constituting the light reflecting optical element in FIG. 6. It is an external appearance perspective view of the 2nd mirror sheet which comprises the light reflection optical element of FIG. FIG. 7 is a top view, a side view, and a front view of a second mirror sheet constituting the light reflecting optical element of FIG. 6. It is a figure explaining the effect | action of the spatial image display apparatus using the light reflection optical element which concerns on embodiment of this invention. In the spatial image display device using the light reflecting optical element according to the embodiment of the present invention, the state where the light from the substance is divided into left and right light and reflected twice by the light reflecting optical element to form a real image, It is the figure seen from the front surface, the side surface, and the upper surface. In the spatial image display device using the light reflecting optical element according to the embodiment of the present invention, the state where the light from the substance is divided into light in the front-rear direction and reflected twice by the light reflecting optical element to form a real image, It is the figure seen from the front surface, the side surface, and the upper surface. It is a figure which shows the horizontal angle dependence of the light utilization efficiency of the light reflection optical element which concerns on embodiment of this invention. It is a figure which shows the perpendicular angle dependence of the light utilization efficiency of the light reflection optical element which concerns on embodiment of this invention. It is a figure which shows the horizontal angle dependence of the light utilization efficiency of the light reflection optical element of FIG. It is a figure which shows the horizontal angle dependence of the light utilization efficiency of the modification of the light reflection optical element which concerns on embodiment of this invention. It is a figure which shows the perpendicular angle dependence of the light utilization efficiency of the modification of the light reflection optical element which concerns on embodiment of this invention. It is a figure which shows the way of the light which enters | separates from the design visual line direction a little, and injects into a light reflection optical element. FIG. 20 is a top view including a reference plane L in FIG. 19, a side view including AA ′ and a normal line m, and a plan view including OC and BB ′. It is explanatory drawing for calculating the thickness of the light reflection optical element which concerns on embodiment of this invention. It is explanatory drawing for calculating the thickness of the light reflection optical element which concerns on embodiment of this invention. It is explanatory drawing for calculating the thickness of the light reflection optical element which concerns on embodiment of this invention. It is a graph which shows the thickness distribution of the horizontal direction of the 1st mirror sheet which comprises the light reflection optical element which concerns on embodiment of this invention, and a perpendicular direction. It is a graph which shows the thickness distribution of the horizontal direction of the 2nd mirror sheet which comprises the light reflection optical element which concerns on embodiment of this invention, and a perpendicular direction.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 6 is an external perspective view of the light reflecting optical element 4 according to the embodiment of the present invention. The light reflecting optical element 4 according to the present embodiment is formed as shown in FIG. 1 to FIG. 3 (however, reference numeral 2 shown in FIG. 1 to FIG. 3 is assigned reference numeral 4 and reference numeral 20 is assigned reference numeral 20). 40, reference numeral 21 is replaced with reference numeral 41, reference numeral 22 is replaced with reference numeral 42, reference numeral 23 is replaced with reference numeral 43, and reference numeral 24 is replaced with reference numeral 44). That is, for a plurality of rectangular parallelepiped materials 40, two opposing surfaces 44 opposite to the surface on which the light reflecting film 43 of one rectangular parallelepiped material 40 is formed and the light reflecting surface 43 of another rectangular parallelepiped material 20 are brought into close contact with each other. The mirror sheets 41 and 42 are formed, and the two mirror sheets 41 and 42 are bonded in a state where one of them is rotated 90 degrees so that the parallel direction of the rectangular parallelepiped material 40 intersects, and the light reflecting optical element 4 is formed. 6 shows the shape of the light reflecting optical element 4 formed by the above method when cut along a plane parallel to the left-right direction and the front-rear direction in FIG. 1 (when cut along the dotted line P in FIG. 1). ing. Here, the front-rear and left-right directions and the direction of AA 'shown in FIG. 1 are the same as the front-rear and left-right directions and the direction of AA' shown in FIG. Specifically, in the present embodiment, the front-rear direction on the bonding surface (hereinafter also referred to as a reference surface) L of the mirror sheets 41 and 42 is defined as the AA ′ direction, and the left-right direction is defined as the BB ′ direction. The mirror sheet 41 is also referred to as a first mirror sheet, the mirror sheet 42 is also referred to as a second mirror sheet, the light reflecting surface 43 of the mirror sheet 41 is a first light reflecting surface, and the light reflecting surface 43 of the mirror sheet 42 is second light reflecting. Also called a surface.

Here, the characteristics of the light reflecting optical element 4 will be described with reference to FIGS. 7 is an external perspective view of the mirror sheet 41, FIG. 8 is a top view, a side view, and a front view of the mirror sheet 41, FIG. 9 is an external perspective view of the mirror sheet 42, and FIG. It is a top view, a side view, and a front view. The design line-of-sight direction S in the present embodiment is, as shown in FIGS. 7 to 10, the AA ′ direction of the reference plane L (from A to A ′, that is, from the front to the back). The direction seen from diagonally above. In the present embodiment, each first light reflecting surface 43 of the mirror sheet 41 is disposed so as to intersect the AA ′ direction and the BB ′ direction at 45 degrees, and each second light reflecting surface of the mirror sheet 42. The surface 43 is orthogonal to the arrangement direction of the first light reflecting surfaces 43 and is arranged to intersect the AA ′ direction and the BB ′ direction at 45 degrees. That is, in the present embodiment, the first light reflecting surfaces 43 of the mirror sheet 41 are arranged from the left back direction to the right front direction so that they are parallel to each other, and the second light reflecting surface 43 of the mirror sheet 42 is also provided. Are arranged from the right back direction to the left front direction so that they are parallel to each other. The longitudinal direction of the light reflecting surfaces 43 constituting the mirror sheets 41 and 42 is the arrangement direction of the light reflecting surfaces 43, and the short direction of the light reflecting surfaces 43 constituting the mirror sheets 41 and 42 is the light. It is the height (thickness) of the reflecting surface 43.

Unlike the light reflecting optical element 2, the light reflecting optical element 4 is characterized in that the thicknesses of the two mirror sheets 41 and 42 are not uniform. That is, the thickness of the mirror sheet 41 on which the first light reflecting surface 43 is arranged from the left back direction toward the right front direction becomes thinner from the left direction toward the right direction as shown in FIGS. Thus, it is formed so as to become thinner from the front direction toward the back direction. On the other hand, as shown in FIGS. 9 and 10, the thickness of the mirror sheet 42 on which the second light reflecting surface 43 is arranged from the right back direction toward the left front direction becomes thinner from the right direction toward the left direction. Thus, it is formed so as to become thinner from the front direction toward the back direction.

Note that the thickness of the mirror sheets 41 and 42 of the light reflecting optical element 4 continuously changes in the left-right direction and the front-rear direction, but to be precise, it is linear as shown in FIGS. Instead of changing to, the curve changes based on the formula (4) relating to the thickness of the light reflecting optical element 4 described later. Various methods are conceivable for producing the light reflecting optical element 4. As an example, the mirror sheets 41 and 42 are formed with the thickness of the thickest part, and then both surfaces of the mirror sheets 41 and 42 are polished and gradually thinned to obtain a desired thickness. Also good.

The operation of the spatial image display device using the light reflecting optical element 4 will be described with reference to FIGS.

As shown in FIG. 11, the line of sight from the observer E is incident on the central part and the peripheral part of the light reflecting optical element 4 on the extension of the spatial image 3, bent by the light reflecting optical element 4, and the spatial image 3. To the substantial part (display part) 1 in a plane symmetrical position with respect to the light reflecting optical element 4. In this case, the thicknesses of the light reflecting surfaces 43 of the mirror sheets 41 and 42 constituting the light reflecting optical element 4 in the front-rear direction and the left-right direction are as shown in FIGS. In the mirror sheets 41 and 42, the light reflected only once increases, while the light transmitted without reflection and the light reflected more than once decrease. Thereby, the luminance distribution of the spatial image 3 observed from the observer E becomes close to the luminance distribution of the entity part 1.

FIG. 12 shows a state in which the light from the entity 1 is divided into left and right light and reflected twice by the light reflecting optical element 4 to form a real image 3 in the spatial image display device using the light reflecting optical element 4. It is the figure seen from the front surface (BB 'cross section), the side surface (AA' cross section), and the upper surface. FIG. 13 shows a state in which the light from the entity 1 is split into light in the front-rear direction and reflected twice by the light reflecting optical element 4 to form a real image 3 in the spatial image display device using the light reflecting optical element 4. FIG. 5 is a view of the above as viewed from the front (BB ′ cross section), the side (AA ′ cross section), and the top surface.

The light emitted from the entity 1 is reflected by the light reflecting surface 43 of the mirror sheet 42 which is the first layer of the light reflecting optical element 4, and is disposed 90 degrees orthogonal to the first layer mirror sheet 42. It is reflected again by the light reflecting surface 43 of the mirror sheet 41 of the second layer, and forms a real image 3 at a position where the reference surface L is symmetrical with the entity 1.

Specifically, as shown in FIG. 12, the light L1 emitted in the left direction from the designed line-of-sight direction S is reflected by the light beam and the mirror sheet 42 compared to the light L2 emitted in the designed line-of-sight direction S. Since the angle formed with the surface 43 is increased, the mirror sheet 42 cannot enter deeper than the light L2 emitted in the design line-of-sight direction S. Therefore, it is necessary to gradually reduce the thickness of the mirror sheet 42 from the design line-of-sight direction S to the left. On the other hand, the light L3 emitted in the right direction from the designed line-of-sight direction S has a smaller angle between the light beam and the light reflecting surface 43 of the mirror sheet 42 than the light L2 emitted in the designed line-of-sight direction S. Therefore, compared with the light L2 emitted in the design line-of-sight direction S, the mirror sheet 42 can be deeply penetrated. Accordingly, it is necessary to gradually increase the thickness of the mirror sheet 42 from the design line-of-sight direction S to the right. From the above, in the present embodiment, with respect to the mirror sheet 42 in which the light reflecting surface 43 is disposed from the right back direction toward the left front direction, the thickness of the mirror sheet 42 from the right direction toward the left direction. Is formed so as to become thinner gradually.

Further, as shown in FIG. 13, the light L4 emitted in the back direction from the design line-of-sight direction S is light and the light reflecting surface of the mirror sheet 42 compared to the light L5 emitted in the design line-of-sight direction S. Since the angle formed with 43 becomes larger, it cannot enter the mirror sheet 42 deeper than the light L5 emitted in the designed line-of-sight direction S. Therefore, it is necessary to gradually reduce the thickness of the mirror sheet 42 from the designed line-of-sight direction S to the back direction. On the other hand, the angle formed between the light reflection surface 43 of the mirror sheet 42 and the light L6 emitted in the near direction from the designed line-of-sight direction S is smaller than the light L5 emitted in the designed line-of-sight direction S. Therefore, compared with the light L5 emitted in the designed line-of-sight direction S, the mirror sheet 42 can be deeply penetrated. Therefore, it is necessary to gradually increase the thickness of the mirror sheet 42 from the design line-of-sight direction S to the front direction. From the above, in the present embodiment, with respect to the mirror sheet 42 in which the light reflecting surface 43 is arranged from the right back direction toward the left front direction, the thickness of the mirror sheet 42 from the front direction toward the back direction. Is formed so as to become thinner gradually.

Although the thickness of the mirror sheet 42 has been described in detail above with reference to FIGS. 12 and 13, the same applies to the thickness of the mirror sheet 41. That is, when the angle formed between the light beam and the light reflection surface 43 of the mirror sheet 41 is increased, the light reflection surface 43 is arranged from the left back direction toward the right front side because it cannot enter the mirror sheet 41 deeply. With respect to the mirror sheet 41, the thickness of the mirror sheet 41 gradually decreases from the left to the right, and the thickness of the mirror sheet 41 gradually decreases from the front to the back. Is formed.

As a result, in the spatial image display device using the light reflecting optical element 4 of the present embodiment, even if the observer shifts the line of sight in the left-right direction with respect to the designed line-of-sight direction S, the spatial image is uniformly bright. Now you can see it. Further, even when the observer shifts his / her line of sight in the front-rear direction with respect to the designed line-of-sight direction S, the viewer can view the spatial image with uniform brightness.

In this embodiment, the mirror sheet 41 is placed on the top and the mirror sheet 42 is placed on the top and bottom. However, as described above, the thickness of the mirror sheet is determined between the light beam and the light reflecting surface 43 of the mirror sheet. Since it is determined according to the angle formed, it may be bonded upside down. In other words, the mirror sheet 42 may be bonded to the top and the mirror sheet 41 may be bonded to the bottom. In this case, the same action is exhibited.

14 and 15 show the light-reflecting optical element 4 of the present embodiment (more precisely, the light-reflecting optical element 4 composed of mirror sheets 41 and 42 whose thickness is calculated based on formula (4) described later). It is a figure which shows the utilization efficiency of light. FIG. 14 is a graph showing the horizontal angle dependency of the ratio (also referred to as transmittance) of the light that is reflected once by the mirror sheets 41 and 42 and passes through the light reflecting optical element 4. FIG. 4 is a graph showing the vertical angle dependence of the ratio of light that is reflected once by the mirror sheets 41 and 42 and passes through the light reflecting optical element 4 (also referred to as transmittance).

In the graph of FIG. 14, the incident angle of 0 degrees in the horizontal direction means the design line-of-sight direction S. Therefore, in FIG. 14, the line of sight is shifted by about ± 15 degrees from the design line-of-sight direction S in the left-right direction. However, the transmittance is almost 100% and does not change, indicating that the brightness of the spatial image is secured.

In the graph of FIG. 15, the incident angle of 45 degrees in the vertical direction means the design line-of-sight direction S. Therefore, FIG. 15 shows the line of sight about ± 15 degrees from the design line-of-sight direction S in the front-back direction. Even if it is shifted, the transmittance is almost 100% and does not change, indicating that the brightness of the spatial image is secured.

On the other hand, FIG. 16 is a diagram showing the light utilization efficiency of the light reflecting optical element 2 in which the thicknesses of the two mirror sheets 21 and 22 are constant. Specifically, it is a graph showing the horizontal angle dependence of the ratio (also referred to as transmittance) of light that is reflected once by the mirror sheets 21 and 22 and passes through the light reflecting optical element 2. FIG. 16 shows that when the light reflecting optical element 2 is used, if the line of sight is shifted from the design line-of-sight direction S to the left-right direction, the transmittance is drastically reduced. Indicates that it is not possible.

17 and 18 are diagrams showing the light use efficiency of the light reflecting optical element 4A in which the thicknesses of the mirror sheets 41A and 42A are changed stepwise instead of continuously. Specifically, the mirror sheets 41A and 42A are formed by changing the thickness in three steps in a stepwise manner in the left-right direction and the front-rear direction. FIG. 17 is a graph showing the horizontal angle dependency of the ratio (also referred to as transmittance) of light that is reflected once by each of the two mirror sheets 41A and 42A and passes through the light reflecting optical element 4A. These are graphs showing the vertical angle dependency of the ratio (also referred to as transmittance) of the light that is reflected once by each of the two mirror sheets 41A and 42A and passes through the light reflecting optical element 4A.

In this case, as shown in FIG. 17, the light reflecting optical element 4A is formed so that three maximum points with a transmittance of 100% appear within ± 15 degrees in the left-right direction from the designed line-of-sight direction S. Therefore, even if the line of sight is shifted about ± 15 degrees in the left-right direction from the design line-of-sight direction S, the brightness of the spatial image can be secured at least 70% in the left-right direction.

Further, in this case, as shown in FIG. 18, the light reflecting optical element 4A is arranged so that three local maximum points with a transmittance of 100% appear within ± 15 degrees in the front-rear direction from the designed line-of-sight direction S. Therefore, even if the line of sight is shifted about ± 15 degrees in the front-rear direction from the designed line-of-sight direction S, the brightness of the spatial image can be secured at least 70% in the front-rear direction.

Next, the thickness D of the mirror sheets 41 and 42 of the light reflecting optical element 4 will be described in detail with reference to FIGS. 19 and 20. FIG. 19 is a diagram showing how the light entering the light-reflecting optical element 4 slightly deviates from the designed line-of-sight direction S, and the traveling direction of the light before the vector OC enters the light-reflecting optical element 4. The traveling direction of the light after the vector CD is incident on the light reflecting optical element 4 is shown. Here, the incident angle of light incident on the light reflecting optical element 4 is γ (specifically, the angle between the normal line m of the reference plane L and the straight line OC), and the outgoing angle is Z (specifically, the normal line of the reference plane L). m and the angle formed by the straight line OD). 20 is a top view including the reference plane L in FIG. 19, a side view including the straight line AA ′ and the normal m, and a plan view including the straight line OC and the straight line BB ′.

As shown in FIG. 19 and FIG. 20, a line of sight OC slightly deviated from the design line of sight direction S is considered. The point C is an intersection of the reference plane L and the line of sight, the straight line AA ′ is a line in the design line of sight direction, and the straight line BB ′ is a line in a direction orthogonal to the line AA ′. That is, the straight line AA ′ and the straight line BB ′ intersect the light reflecting surfaces 43 of the two mirror sheets 41 and 42 constituting the light reflecting optical element 4 at an angle of 45 degrees. At this time, an angle at which the plane including the straight line BB ′ and the normal line m intersects with the plane including the line of sight OC and the straight line BB ′ is α, the plane including the straight line AA ′ and the normal line m, the line of sight OC and the normal line m Let β be the angle at which the included planes intersect. Further, the refractive index in the light reflecting optical element 4 is n, and the mirror interval between the light reflecting surfaces 43 in the mirror sheets 41 and 42 constituting the light reflecting optical element 4 is W.

となり、式（１）～（３）から、

が導かれる。 Then

From equations (1) to (3),

Is guided.

Here, the formation of equations (1) to (3) will be described in detail.

First, Equation (3) is considered in the coordinate system of FIG. First, light traveling in the medium having a refractive index n = 1 is indicated by a straight line df. At this time, the angle formed by the straight line df and the z axis is γ, the angle formed by the straight line de and the z axis projected from the straight line df on the xz plane is α, and the angle formed by the straight line df and the straight line de is β (FIG. 21). Α, β, and γ correspond to α, β, and γ in FIGS. 19 and 20). Further, the height of the rectangular parallelepiped formed by the straight line df and the straight line de is set to 1, the plane intersecting the x axis and the y axis at 45 degrees and orthogonal to the xy plane is defined as the light reflecting surface 43. .

In the right triangle aed, from ad = tan α, de = 1 / cos α. On the other hand, in the right triangle def, ef = tan β / cos α from ef = de × tan β.

Therefore, in the light reflecting surface 43 passing through the vertex f, if the intersection of the light reflecting surface 43 and the x axis is P, OP = he + eP = tan α + tan β / cos α.

のときである。すなわち、原点ｈを通る光反射面４３の上端を入射してきた光ｄｆがｆを通る光反射面４３の下端に反射されるのであれば、入射角γで入射した光はすべて第１層目の光反射面４３において１回反射されることとなる。したがって、屈折率１のときの光反射面４３の高さをＤ１とすると、

　よって、

　次に、屈折率１の媒体から屈折率ｎの媒体に光が進入する場合を考える。図２２は、図２１において直線ｄｆ及びｚ軸を含む平面Ｑ上の光の進み方を示している。ここで、平面Ｑ上における光反射面４３の間隔をＶ、屈折率ｎのときの光反射面４３の高さをＤｎとして、屈折率１の媒体から屈折率ｎの媒体に光が進入する場合のｈｆ方向に対するｚ軸方向の距離を考えると、ｔａｎγ＝Ｖ／Ｄ１、ｔａｎＺ＝Ｖ／Ｄｎであるから、

　この結果、式（５）及び式（６）より、式（３）は成立する。 Now, assuming that the interval between the light reflecting surfaces 43 is W, the desired z-axis height D1 is:

At the time. That is, if the light df incident on the upper end of the light reflecting surface 43 passing through the origin h is reflected on the lower end of the light reflecting surface 43 passing through f, all the light incident at the incident angle γ is in the first layer. It is reflected once at the light reflecting surface 43. Therefore, when the height of the light reflecting surface 43 when the refractive index is 1 is D1,

Therefore,

Next, consider a case where light enters from a medium having a refractive index of 1 into a medium having a refractive index of n. FIG. 22 shows how light travels on the plane Q including the straight line df and the z axis in FIG. Here, when the distance between the light reflecting surfaces 43 on the plane Q is V, and the height of the light reflecting surface 43 when the refractive index is n is Dn, light enters from the medium having the refractive index 1 to the medium having the refractive index n. Considering the distance in the z-axis direction with respect to the hf direction, tan γ = V / D1 and tanZ = V / Dn.

As a result, Expression (3) is established from Expression (5) and Expression (6).

Next, regarding equation (1), considering the distance traveled by light, tan γ is a combined vector of tan α and tan β as shown in FIG.

が成り立つ。また、式（１）からは、

であるから、式（７）のγに式（８）を代入すると、式（２）は成立する。 In addition, with respect to the equation (2), from Snell's law, 1 · sinγ = n · sinZ.

Holds. Also, from equation (1),

Therefore, when equation (8) is substituted into γ of equation (7), equation (2) is established.

Finally, regarding Expression (4), Expression (4) is established by substituting Expression (7) and Expression (8) into Expression (3).

であり、スネルの法則から、

となる。なお、式（９）及び（１０）は、特許文献２にて本出願人がすでに開示している式である。 It should be noted that when β = 0 in the expression (3), that is, when viewed from the design line-of-sight direction S (when γ = α, Z = X),

From Snell's law,

It becomes. Expressions (9) and (10) are expressions already disclosed by the present applicant in Patent Document 2.

24 is a graph showing the horizontal and vertical thickness distribution of the mirror sheet 41 calculated based on the formula (4), and FIG. 25 is a horizontal direction of the mirror sheet 42 calculated based on the formula (4). It is a graph which shows thickness distribution of a perpendicular direction. As shown in FIG. 24, in the mirror sheet 41 in which the first light reflecting surface 43 is arranged from the left back direction toward the right front direction, the thickness of the mirror sheet 41 is thin from the left direction toward the right direction. And is formed so as to become thinner from the near side toward the far side. On the other hand, as shown in FIG. 25, in the mirror sheet 42 in which the second light reflecting surface 43 is arranged from the right back direction toward the left front direction, the thickness of the mirror sheet 42 is from the right direction to the left direction. It is formed so as to become thinner and thinner from the near side toward the far side.

As described above, according to the present embodiment, in the first mirror sheet 41 and the second mirror sheet 42 constituting the light reflecting optical element 4, the design is directed from the left back direction to the right front direction with respect to the design line-of-sight direction S. The thickness of the mirror sheet 41 on which the first light reflecting surface 43 is disposed is formed so as to be gradually reduced from the left direction to the right direction, and to the right rear with respect to the design line-of-sight direction S. Since the thickness of the mirror sheet 42 on which the second light reflecting surface 43 is arranged from the direction toward the left front direction is formed so as to gradually become thinner from the right direction toward the left direction, the design line of sight Even if the line of sight is shifted in the left-right direction from the direction S, the brightness of the spatial image can be ensured.

Further, in the first mirror sheet 41 and the second mirror sheet 42 constituting the light reflecting optical element 4, the first light reflecting surface 43 is arranged from the left rear direction toward the right front direction with respect to the design line-of-sight direction S. The thickness of the mirror sheet 41 and the thickness of the mirror sheet 42 on which the second light reflecting surface 43 is arranged from the right back direction toward the left front direction with respect to the designed line-of-sight direction S are Since it is formed so as to gradually become thinner from the front direction toward the back direction, the brightness of the spatial image can be ensured even if the line of sight is shifted from the designed line-of-sight direction S to the front-rear direction.

Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments, and various modifications can be made to the embodiments of the present invention without departing from the gist of the present invention. Such modifications and changes can be made, and those accompanying such modifications and changes are also included in the technical scope of the present invention.

1 Real part (object, display part)
2,4,4A Light reflecting optical element (mirror)
3 Real image (spatial image)
20, 40 rectangular parallelepiped material 21, 22, 41, 42, 41A, 42A mirror sheet 23, 43 light reflecting surface

Claims (5)

A spatial image display device including a light reflecting optical element that reflects light from an entity toward an observer,
The light reflecting optical element is
The first assembly and the second assembly in which a plurality of longitudinal members having one light reflecting surface are arranged so that the light reflecting surfaces are in the same direction are overlapped so that the light reflecting surfaces are orthogonal to each other. ,
Each of the plurality of longitudinal members constituting the first assembly and the second assembly comprises a light-transmitting rectangular parallelepiped having four surfaces extending in the longitudinal direction, and one of the four surfaces is the surface A light reflecting surface,
In each of the first aggregate and the second aggregate, the rectangular parallelepiped is arranged so that the light reflecting surface of one of the rectangular parallelepiped and the surface facing the light reflecting surface of the adjacent rectangular parallelepiped contact each other,
The light from the entity part is reflected once on each of the light reflecting surfaces of the first aggregate and the second aggregate to form a real image,
The light reflecting surface of the first aggregate is arranged obliquely from the left back direction toward the right front side when viewed from the line of sight of the observer, and the light reflecting surface of the second aggregate is In the case of being arranged obliquely from the right back direction toward the left front direction as seen from the observer's line of sight,
The thickness of the first aggregate, which is the length in the short direction of the light reflecting surface of the first aggregate, is formed so as to decrease from the left to the right as viewed from the line of sight of the observer. And the thickness of the second aggregate, which is the length in the short direction of the light reflecting surface of the second aggregate, is from the right to the left as viewed from the observer's line of sight. A spatial image display device formed to be thin. The light reflecting surface of the first aggregate is arranged obliquely from the left back direction toward the right front side when viewed from the line of sight of the observer, and the light reflecting surface of the second aggregate is In the case of being arranged obliquely from the right back direction toward the left front direction as seen from the observer's line of sight,
2. The spatial image according to claim 1, wherein the thickness of each of the first aggregate and the second aggregate is formed so as to become thinner from the back direction toward the near side when viewed from the line of sight of the observer. Display device. The spatial image display device according to claim 2, wherein the thicknesses of the first aggregate and the second aggregate are formed so as to continuously change in the front-rear and left-right directions when viewed from the line of sight of the observer. 3. The space according to claim 2, wherein the thicknesses of the first aggregate and the second aggregate are formed to change stepwise in the front-rear and left-right directions when viewed from the observer's line of sight. Video display device. The affixing surface when the first aggregate and the second aggregate are overlapped is defined as a reference plane L, the observer's line-of-sight position is O, and the intersection between the observer's line-of-sight direction and the reference plane L is C, A straight line that intersects each of the light reflecting surfaces of the first aggregate and the second aggregate at 45 degrees on the reference plane L is AA ′, a straight line that is orthogonal to the straight line AA ′ on the reference plane L is BB ′, and a straight line BB ′ And the plane formed by the plane including the normal m of the reference plane L and the plane including the line of sight OC and the straight line BB ′ is α, the plane including the straight line AA ′ and the normal m, and the plane including the line of sight OC and the normal m Is an optical refractive index of the light reflecting optical element is n, and an interval between the light reflecting surfaces of the first aggregate and the second aggregate is W, the first aggregate and the The thickness D of each second assembly is

The spatial image display device according to any one of claims 1 to 4, expressed as:

Images