JP7818285B2 - aerial projection device - Google Patents

Description

The present invention relates to an aerial projection device.

There is a demand for aerial projection devices that can project images of buttons in the air, such as those used to make elevators and other facilities contactless to prevent the spread of infectious diseases, or that can project predetermined images in the air for educational or gaming purposes. For example, Patent Document 1 listed below describes an aerial image forming device that can project an image displayed on a display device into the air. In this aerial image forming device, light output from the display device is reflected by a beam splitter toward a retroreflective sheet, and the light retroreflected by this retroreflective sheet passes through the beam splitter to form an image in the air. Patent Document 2 listed below also describes a spatial display device that can project an image displayed on an image display unit into the air. In this spatial display device, light output from the image display unit is reflected by a selective reflective film toward a retroreflective material, is retroreflected by the retroreflective material, and passes through the selective reflective film to form an image in the air.

Japanese Patent Application Laid-Open No. 2019-207574 JP 2018-92000 A

The aerial image forming devices and spatial display devices described in the aforementioned Patent Documents 1 and 2 allow images displayed on a display device or image display unit to be displayed in mid-air. However, as described in Patent Document 2, the display device or image display unit is required to emit image light containing three-dimensional position information, resulting in a complex structure. For example, the image display unit in Patent Document 2 has a microlens array arranged on the display surface of a display panel such as a liquid crystal display panel. Aerial image forming devices and spatial display devices that use image display means with such a complex structure tend to be complex overall.

The present invention has been made to solve the above-mentioned problems, and aims to provide an aerial projection device that can display images in the air using an image display means with a simple structure.

The aerial projection device of the present invention, which has been devised to achieve the above-mentioned objectives, comprises a holographic projector unit that emits diffracted light obtained by diffracting irradiated parallel light based on interference information of a hologram of a predetermined image; a screen onto which the diffracted light is irradiated and the predetermined image is projected; a projection unit that comprises a half mirror that is installed at an angle relative to the diffracted light irradiated onto the screen and at a position where transmitted diffused light that has passed through the screen and diffused is irradiated; and a retroreflection element onto which the transmitted light or reflected light from the half mirror is irradiated. The transmitted or reflected light from the half mirror of the transmitted diffused light is retroreflected by the retroreflection element and emitted in the opposite direction along the original incident path, and a real image of the predetermined image is formed in the air on one side of the half mirror by the reflected light reflected by the half mirror or the transmitted light that has passed through the half mirror.

By positioning the screen in front of or behind the specified position where the real image is projected based on the interference information of the hologram so that the real image appears blurred, the range of expression of the aerial projection device can be expanded.

The retroreflective element is tilted so that the virtual image corresponding to the real image visible on the other side of the half mirror moves out of the field of view due to specular reflection from the retroreflective element, allowing the real image to be clearly visible.

The holographic projector unit emits diffracted light based on the interference information of each hologram of at least two predetermined images. The diffracted light based on the interference information of one of the predetermined images is irradiated onto the screen and projected into the air via the half mirror and the retroreflective element, forming a real image of one of the predetermined images. The diffracted light based on the interference information of the other of the predetermined images passes through the half mirror without being irradiated onto the screen and is irradiated onto the retroreflective light emission surface of the retroreflective element, projecting the other of the predetermined images. At the same time, the retroreflective light emitted from the retroreflective light emission surface is reflected by the half mirror, creating a virtual image of the other of the predetermined images in the air on the side opposite the reflective surface of the half mirror, allowing the real and virtual images to be recognized simultaneously.

By positioning the screen and/or the retroreflective element in a position forward or rearward of the predetermined position where the real image and/or virtual image are projected based on the interference information of the hologram so that the real image and/or virtual image appear blurred, one or both of the real image and virtual image can be made to appear blurred, further expanding the range of expression of the aerial projection device.

The screen is a stereoscopic screen, allowing a three-dimensional image to be formed in the air.

The screen is made of Japanese paper or nonwoven fabric, making it easy to create screens such as three-dimensional screens.

At least two pairs of combinations of the half mirror and the screen are provided, and the two pairs are installed in series at a predetermined interval so that the real image is formed in the air on the same side of each of the half mirrors, thereby making it possible to form a complex real image in the air.

The screen onto which the projected image corresponding to one of the real images formed in the air on the same side of each of the half mirrors is projected from the holographic projector unit is movable in a direction toward or away from the half mirror so that at least one of the real images moves toward or away from the half mirror.By moving the screen in a direction toward or away from the half mirror, the real images can be moved toward or away from each other or one real image can be made to move behind the other real image.

It is preferable that the hologram is a computer-generated hologram and a spatial light modulator is provided that modulates the parallel light into diffracted light based on the interference information of the computer-generated hologram, as this makes it easy to create the desired hologram.

The computer-generated hologram is an amplitude hologram, and the amplitude hologram is expressed by the following formula (1):
The calculation speed of the amplitude hologram can be increased by calculating based on

The computer-generated hologram is a phase hologram, and the phase hologram is expressed by the following formula (2):
Since the calculation is based on the above, the calculation speed of the phase hologram can be increased.

The aerial projection device of the present invention can have a simple structure in which the image display means consists of a hologram on which interference information of a predetermined image is recorded, and a screen that has both translucent and diffusive properties and onto which the predetermined image is projected by irradiating diffracted light based on the interference information of this hologram, thereby allowing the device as a whole to have a simple structure.

1 is a schematic diagram illustrating an aerial projection device to which the present invention is applied. 10 is a schematic diagram illustrating another aerial projection device to which the present invention is applied. FIG. 10 is a schematic diagram illustrating another aerial projection device to which the present invention is applied. FIG. 10 is an explanatory diagram illustrating the state of a real image when the position of the screen is moved in another aerial projection device to which the present invention is applied. FIG. 10 is an explanatory diagram illustrating the movement of a virtual image that is visually recognized in correspondence with a real image when the retroreflective element is tilted in another aerial projection device to which the present invention is applied. FIG. 10 is a schematic diagram illustrating another aerial projection device to which the present invention is applied, in which a real image and a virtual image can be simultaneously viewed. FIG. 1 is a schematic diagram illustrating the state of a real image and a virtual image when a retroreflective sheet is moved in an aerial projection device to which the present invention is applied, in which a real image and a virtual image can be simultaneously viewed. 1 is a schematic diagram illustrating an aerial projection device to which the present invention is applied, in which a real image and a virtual image can be simultaneously viewed, in which a retroreflective sheet is divided and arranged when a flat screen is used. FIG. 1 is a schematic diagram illustrating an aerial projection device to which the present invention is applied, in which a real image and a virtual image can be simultaneously viewed using a three-dimensional screen, in which a retroreflective sheet is divided and arranged. 1 is a schematic diagram illustrating a device for measuring the visible light transmittance and diffusivity of a material used in a screen. 1 is a schematic diagram illustrating an aerial projection device that allows multiple virtual images to be simultaneously viewed in the air. FIG. 12 is a perspective view illustrating the installation state of a retroreflective sheet used in the aerial projection device shown in FIG. 11. 12 is a schematic diagram illustrating how a virtual image appears when a light-blocking object is placed on the other side of the second half mirror that constitutes the aerial projection device shown in FIG. 11 . 12A and 12B are schematic diagrams illustrating the movement of a virtual image when one of the two retroreflective sheets used in the aerial projection device shown in FIG. 11 is moved in the vertical direction. 12 is a schematic diagram illustrating the movement of a virtual image when the optical path from one half mirror 30 of the two retroreflective sheets used in the aerial projection device shown in FIG. 11 is lengthened. FIG. 12 is a schematic diagram illustrating the movement of a virtual image when the aerial projection device shown in FIG. 11 uses one retroreflective sheet and the retroreflective sheet is movable. FIG. 12 is a schematic diagram illustrating how a virtual image appears when two retroreflective sheets used in the aerial projection device shown in FIG. 11 are arranged side by side in the left and right directions of a rectangular half mirror. FIG. Fig. 18(a) is a schematic diagram illustrating a guide device for guiding a three-dimensional screen to the projection position of a holographic projector unit of an aerial projection device, Fig. 18(b) is a perspective view showing the projection state when the three-dimensional screen is positioned at the projection position of the holographic projector unit, and Fig. 18(c) is a perspective view showing the projection state when the three-dimensional screen is deviated from the projection position of the holographic projector unit. FIG. 19(a) is a front view showing the projection state when a flat screen is positioned at the projection position of the holographic projector unit, and FIG. 19(b) is a front view showing the projection state when the flat screen is shifted from the projection position (focal position) of the holographic projector unit. 19 is a schematic diagram illustrating an example in which the guide device shown in FIG. 18 is used in a personal authentication device. FIG. 20 is a schematic diagram illustrating an example in which the guide device shown in FIG. 18 is used in another personal authentication device. FIG. 1 is a conceptual diagram for explaining the principle of creating a computer-generated hologram. 3 is a schematic diagram illustrating the configuration of a CGH calculation unit that calculates an amplitude hologram. FIG. 10 is a pseudocode for calculating an amplitude hologram. 1 is a flowchart for calculating an amplitude hologram. FIG. 2 is a schematic diagram illustrating the configuration of a CGH calculation unit that calculates a phase hologram. 1 is a pseudocode for calculating a phase hologram. 1 is a flowchart for calculating a phase hologram. FIG. 29(a) is another pseudo-code for calculating an amplitude hologram, and FIG. 29(b) is another pseudo-code for calculating a phase hologram. FIG. 4 is a schematic diagram illustrating an arrangement of three projection units 10b of the aerial projection device shown in FIG. 3. 31 is a schematic diagram illustrating the direction in which a real image moves when the frame 26 of the projection unit 10b-2 of the two projection units 10b-1 and 10b-2 shown in FIG. 30 is moved in the up-down direction.

The present invention is described in detail below, but the scope of the present invention is not limited to these.

An aerial projection device to which the present invention is applied is shown in Figure 1(a). The aerial projection device 10 shown in Figure 1(a) is composed of a holographic projector unit 10a and a projection unit 10b. The holographic projector unit 10a is composed of a personal computer (PC) 12 to which a tablet terminal device 11 is connected, a reflective spatial light modulator (SLM) 14, a first half mirror 22, and a parallel light emitter 15. The parallel light emitter 15 is composed of a laser light emitter 16, an objective lens 18, and a plano-convex lens 20. In the holographic projector unit 10a, a computer-generated hologram (CGH) of a cube as a predetermined image input from the tablet terminal device 11 is calculated by the CGH calculation unit 17 of the PC 12 and displayed on the SLM 14. The interference fringes displayed on the SLM 14 are interference information hologrammed so that the cube is projected at a predetermined position. Parallel light is irradiated onto the display surface of the SLM 14 on which such interference fringes are displayed. This parallel light is laser light emitted from the laser light emitting unit 16 of the parallel light emitting unit 15, which is first focused by the objective lens 18 and then spreads, becomes parallel light by the plano-convex lens 20, and is reflected by the first half mirror 22 toward the display surface of the SLM 14. The parallel light irradiated onto the display surface of the SLM 14 becomes diffracted light that is diffracted based on the hologram interference information displayed on the display surface, emerges from the display surface of the SLM 14, passes through the first half mirror 22, and is emitted to the projection unit 10b.

Projection unit 10b is composed of a mirror 24, a horizontally placed frame 26, a three-dimensional screen 28 supported by a support base 27 placed on the frame portion of frame 26, a second half mirror 30 tilted at a 45° angle (tilt angle 45°) relative to frame 26, and a retroreflective sheet 32 positioned opposite frame 26 as a retroreflective element. Diffracted light incident on projection unit 10b from holographic projector unit 10a is reflected by mirror 24 placed at a 45° tilt angle, passes through the hollow portion of frame 26, and illuminates three-dimensional screen 28. Three-dimensional screen 28 is formed in a shape similar to the cube that is the predetermined image calculated for the computer-generated hologram, and is supported by support base 27 at a predetermined position that was the premise for calculating the computer-generated hologram.

As shown in FIG. 1(b), the three-dimensional screen 28 is formed by attaching Japanese paper 28c (Tengu paper: basis weight 18 g/ ^m2 ) to a frame 28b. The Japanese paper 28c has a transmittance of 55% or more at the optical axis of the irradiated visible light (green laser light with a wavelength of 532 nm). As shown in FIG. 1(a), the diffusivity of the transmitted light from the irradiated visible light that passes through the Japanese paper 28c at a height between the top of the three-dimensional screen 28 and the midpoint of the second half mirror 30 is 15% or more at a range of -10° to +10° relative to the optical axis of the visible light (green laser light with a wavelength of 532 nm). Such Japanese paper 28c forms three faces of a cube, and as shown in FIG. 1(a), the three faces to which the Japanese paper 28c is attached are supported by a support base 27 so that they face the frame 26. When diffracted light is irradiated onto such a three-dimensional screen 28, a hologram-like projection image 28a of the cube is projected. The Japanese paper 28c forming the three surfaces of the three-dimensional screen 28 is a transmissive diffuser that transmits and diffuses at least a portion of the irradiated diffracted light, so that, as shown in Figure 1(a), for example, light transmitted through each of the projection points 29a, 29a of the cubic projection image 28a is diffused and becomes transmitted diffused light. This transmitted diffused light passes through the second half mirror 30 and is incident on the retroreflective sheet 32.

As shown in FIG. 1(c), the retroreflective sheet 32 has numerous glass beads 33b arranged in a transparent resin layer 33c formed on one side of the reflective sheet 33a. As shown in FIG. 1(c), the retroreflective sheet 32 retroreflects light by emitting outgoing light in the opposite direction to the incident light, along the path of the incident light. Diffused light incident on the retroreflective sheet 32 is emitted in the opposite direction along the path of the incident light, as shown in FIG. 1(a), and is reflected by the second half mirror 30, forming a three-dimensional real image 34 of a cube in the air on one side of the second half mirror 30. Projection points 29a and 29b of the cube image 28a projected onto the 3D screen 28 correspond to image points 34a and 34b of the real image 34. The real image 34 shown in FIG. 1(a) is viewed from the side, and an enlarged view of the real image 34 viewed from the front is shown in FIG. 1(d). Points 34a and 34b shown in Figure 1(d) correspond to the image points 34a and 34b of the real image 34 shown in Figure 1(a). While the real image 34 shown in Figure 1 is a cube, if its shape is changed to another shape, the other shape can be input from the tablet terminal device 11 to the PC 12, and a computer-generated hologram of the other shape can be calculated by the PC 12, which can then easily display the other shape as interference fringes on the SLM 14. The same applies when adding a pattern to a shape. While the retroreflective sheet 32 shown in Figure 1(c) uses a large number of glass beads 33b, it may also be a retroreflective sheet using a large number of prisms.

The projection unit 10b of the aerial projection device 10 shown in Figure 1 is arranged parallel to the frame 26, which has the retroreflective sheet 32 arranged horizontally, but the retroreflective sheet 32 may also be arranged perpendicular to the frame 26, as shown in Figure 2. In this case, the real image 34 is also formed at approximately the same aerial position as the projection unit 10b shown in Figure 1. However, in this case, when the real image 34 is viewed from the front, the image reflected by the retroreflective sheet 32 may come into view.

In Figures 1 and 2, a three-dimensional screen 28 is used, but as shown in Figure 3, a flat screen 36 (hereinafter simply referred to as screen 36) can also be created by attaching the peripheral edge of a sheet of Japanese paper to the frame of frame 26. The projected image 36a projected onto such a single screen 36 is a two-dimensional image (triangle) as shown in Figure 3(b), and the real image 38 formed in the air is also a two-dimensional image. Figure 3(c) shows the shape of the real image 38 (triangle) formed in the air as viewed from the front. Figure 3(c) shows image points 38a and 38b of real image 38 corresponding to projection points 37a and 37b of projected image 36a shown in Figures 3(a) and (b).

In the aerial projection device 10 shown in Figures 1 to 3, the interference fringes displayed on the SLM 14 of the holographic projector unit 10a are computer-generated holograms (CGHs) calculated by the CGH calculation unit 17 of the PC 12 so that a predetermined image is clearly projected onto the installed 3D screen 28 or 36, in other words, so that the image is in focus on the 3D screen 28 or 36. If the frame 26 on which the screen 36 in Figure 3(a) is mounted is moved to position 26' on the second half mirror 30 side as shown in Figure 4(a), i.e., further back than the CGH's focal position, without changing the focal position of the CGH, the projected image 36a' (two-dimensional image (triangle)) projected onto the screen 36 will be blurred as shown in Figure 4(b), and the resulting real image 38' will also be blurred as shown in Figure 4(c). Moreover, this real image 38' will be focused closer to the second half mirror 30 as shown in Figure 4(a). In this way, simply by moving the position of the screen 36, the aerial image can be made blurred, thereby expanding the range of aerial image representation. For example, by gradually moving the screen 36 away from the second half mirror 30, the aerial image can be made to change from a blurred shape located far away to a clear shape located close by, making it possible to represent an object moving from far to close. In Figure 4, the position of the screen 36 is moved behind the focal position of the CGH. However, if the screen 36 is moved forward (toward the mirror 24) from the focal position of the CGH, the real image 38' will also be blurred. However, in this case, the distance between the real image 38' and the second half mirror 30 is wider than the distance between the real image 38 and the second half mirror 30. Note that while Figure 4 shows an example of a screen 36, the same effect can be achieved with the 3D screen 28 by moving its position.

In the retroreflective sheet 32 shown in Figures 1 to 4, a portion of the irradiated diffracted light is specularly reflected, resulting in a virtual image 39 corresponding to the real image 38 being visible on the other side of the second half mirror 30, as shown in Figure 5(a). This virtual image 39 is not a problem when the real image 38 is clear, but if the real image 38 becomes slightly unclear, the virtual image 39 may become an eyesore. In such cases, tilting the retroreflective sheet 32 as shown in Figure 5(b) moves the virtual image 39 out of the field of view without changing the position of the real image 38, ensuring that the real image 38 is reliably visible. The retroreflective sheet 32 shown by the solid line in Figure 5(b) is tilted so that the real image 38 side (the front side from the viewer's perspective) is lower, in which case the virtual image 39' moves downward. On the other hand, the retroreflective sheet 32' shown by the dashed line in Figure 5(b) is tilted so that the real image 38 side is higher, in which case the virtual image 39" moves upward. Figure 5 shows the case where the retroreflective sheet 32 is tilted back and forth, but if the retroreflective sheet 32 is tilted left and right, the virtual image 39 can also move left and right and be outside the field of view.

1 to 5 have described an aerial projection device that projects a real image in the air. However, the CGH calculation unit 17 of the PC 12 that constitutes the holographic projector unit 10a can simultaneously display the interference information of each hologram for multiple predetermined images on the SLM 14. This allows the holographic projector unit 10a to simultaneously emit diffracted light diffracted based on the interference information of each hologram for at least two predetermined images. Therefore, as shown in Figure 6(a), a portion of the diffracted light based on the interference information of one of the predetermined images is irradiated onto the screen 36 placed on the frame 26 to project the projected image 36a. The transmitted and diffused light that passes through the screen 36 passes through the second half mirror 30 and the retroreflective sheet 32, which serves as a retroreflective element, and is projected in the air as a real image 38, one of the predetermined images. At the same time, diffracted light based on the interference information of the other side of the predetermined image is transmitted through the second half mirror 30 and irradiated onto the retroreflected light exit surface of the retroreflecting sheet 32 without being irradiated onto the screen 36, thereby projecting the other side of the predetermined image 40. The retroreflected light from each of the projection points 40a and 40b of the projected image 40 on the retroreflected light exit surface is reflected by the second half mirror 30, allowing a virtual image 42 of the other side of the predetermined image to be viewed in the air on the side opposite the reflective surface of the second half mirror 30. Points 42a and 42b shown in Figure 6 correspond to the projection points 40a and 40b of the projected image 40. Thus, with the aerial projection device 10 shown in Figure 6(a), the real image 38 and the virtual image 42 can be viewed simultaneously, as shown in Figure 6(b). In the aerial projection device 10 shown in FIG. 6, the focal position of one CGH for the predetermined image is the screen 36, and the focal position of the other CGH for the predetermined image is the retroreflection sheet 32.

Even with the aerial projection device 10 shown in Figure 6, by moving only the screen 36 forward or backward from the CGH's focal position as shown in Figure 4 without changing the CGH's focal position, it is possible to maintain a clear virtual image 42 and blur only the real image 38. Furthermore, by moving the retroreflective sheet 32 to position 32' behind the CGH's focal position as shown in Figure 7(a), the projected image 40' projected onto the retroreflective sheet 32 becomes blurred, resulting in a blurred virtual image 42' as shown in Figure 7(b). Because the gap between the retroreflective sheet 32 and the second half mirror 30 widens when moved to position 32', the virtual image 42' is positioned farther from the second half mirror 30 than the virtual image 42, as shown in Figure 7(a). Because the position of the screen 36 does not change, the real image 38 remains clear and is formed at the same position. The points 42a' and 42b' shown in FIG. 7A correspond to the projected points 40a' and 40b' of the retroreflective sheet 32 that has been moved to the position 32'.

As shown in Figure 8, by dividing the sheet into a retroreflective sheet 32a for real images and a retroreflective sheet 32b for virtual images, it is possible to move only the retroreflective sheet 32b, blur only the virtual image 42, and move its position. Also, if you want to blur only the real image 38, this can be achieved by moving the position of the screen 36. While Figure 8 shows an example of a screen 36, even when a 3D screen 28 is used, by dividing the sheet into a retroreflective sheet 32a for real images and a retroreflective sheet 32b for virtual images, as shown in Figure 9, it is possible to move only the retroreflective sheet 32b, blur only the virtual image 42, and move its position.

In the above explanation, the 3D screen 28 or screen 36, or the retroreflective sheet 32, was moved without changing the focal position of the CGH to blur the real image 34 (3D screen 28) or real image 38 (screen 36) and/or virtual image 42, and their positions were also moved. However, by changing the focal position of the CGH, it is possible to blur the real image 38 and/or virtual image 42 without changing their positions and without moving the screen 36 or 3D screen 28, or the retroreflective sheet 32. Because the CGH is calculated by the CGH calculation unit 17 of the PC 12, the focal position of the CGH can be changed quickly.

The Japanese paper 28c used in the three-dimensional screen 28 or screen 36 of the aerial projection device 10 shown in Figures 1 to 9 has a transmittance of 55% or more at the optical axis of the irradiated visible light (green laser light with a wavelength of 532 nm), and a diffusion rate of 15% or more over the entire range of -10° to +10° relative to the optical axis of the visible light at the height between the top of the three-dimensional screen 28 and the midpoint of the second half mirror 30 as shown in Figure 1. Measurement of such visible light transmittance was performed using the measuring device shown in Figure 10. The measuring device shown in Figure 10 is composed of a light source 50 that emits visible light such as laser light, an objective lens 52, a plano-convex lens 54, a plate-like body 56 with a hole 58 of a predetermined diameter opened in its center, and a light receiving surface 62 of an actinometer (laser power meter). The plate-like body 56 is erected at a distance L from the light source 50 so that the centerline of the hole 58 coincides with the optical axis 51 of the laser light from the light source 50. The light receiving surface 62 of the actinometer is disposed at a position where the distance M from the plate-like body 56 is equal to the height from the screen to the midpoint of the second half mirror 30, so that the hole 58 and the light receiving surface 62 of the actinometer face each other. When the screen is a three-dimensional screen 28 as shown in FIG. 1 , this distance M is the height between the top edge of the three-dimensional screen 28 and the midpoint of the second half mirror 30 (the height indicated as M in FIG. 1 ). Furthermore, the light receiving surface 62 of the actinometer is disposed so as to be rotatable about the center line of the hole 58 as shown in FIG. 10 . The radius of rotation of the light receiving surface 62 is the distance M. In the measuring device shown in FIG. 10 , light emitted from the light source 50 is first focused by the objective lens 52, then spreads, is converted into parallel light by the plano-convex lens 54, and irradiates the hole 58 in the plate-like body 56. The amount of light transmitted through the hole 58 is received and measured by the light receiving surface 62 of the actinometer. This measurement was performed by first bringing the light receiving surface 62 of the actinometer into contact with the plate-like body 56 so as to close the hole 58 (M = 0 cm in FIG. 10). The amount of light transmitted at this time was defined as _T0 . Next, the measurement object 60 was attached so as to close the hole 58, and the amount of light received that had passed through the hole 58 and the screen material, measured by the actinometer with the light receiving surface 62 placed in a position facing the hole 58 (M = 0 cm), was defined as T. The transmittance was defined as (T/ _T0 ) x 100.
Furthermore, the distance between the light receiving surface 62 of the actinometer and the screen material attached to the hole 58 is always kept at 15 cm (rotation radius of the light receiving surface 62: 15 cm), and the light receiving surface 62 of the actinometer is rotated by a predetermined angle ±θ with respect to the optical axis 51 to measure the amount of received light at position 62'. This amount of received light is the amount of diffusion (T') that has passed through the measurement object 60 and diffused in the angle ±θ directions. The diffusion coefficient is the ratio (T'/ _T1 ) to the amount of received light ( _T1 ) measured at an angle of 0° x 100.

Measurements using the measuring device shown in Figure 10 show that a screen with a transmittance of at least 47% along the optical axis of irradiated visible light is particularly preferred, as it allows for a clear view of the real image formed in the air, even in bright rooms. Screens with a transmittance of less than 47% tend to make the real image formed in the air significantly less visible in bright rooms, but the real image is visible in dark rooms. Examples of screen materials with a visible light transmittance of 47% or more include woven fabrics, nonwoven fabrics, Japanese paper, and diffusion plates made of resins such as acrylic (FANTAREX DREAM D-710M, FANTAREX DREAM D-709M (both trade names) manufactured by Nitto Jushi Kogyo Co., Ltd., and DF-LFV3-100 (trade name) manufactured by CCS Inc.). A transmittance of 55 to 65% is preferred. Even with a screen with a transmittance of more than 65%, such as a transparent screen made of a transparent film, a real image is formed in the air, but a virtual image caused by the retroreflection of the retroreflective material is simultaneously visible, making the real image difficult to see. However, as described above, by tilting the retroreflective element, the virtual image can be moved left and right or forward and backward to be outside the field of view so that only the real image is in the field of view. In addition, the virtual image can sometimes be eliminated by covering the periphery of the mirror 24 with a light-shielding mask to block excess diffracted light that passes through the second half mirror 30 and illuminates the retroreflective sheet 32 without being irradiated onto the screen.

At a height M from the top of the three-dimensional screen 28 shown in FIG. 1 to the midpoint of the second half mirror 30, a screen with a diffusion rate of at least 15% across the entire range of -10° to +10° relative to the optical axis of the irradiated visible light can be preferably used. A screen with such a diffusion rate can form a clear real image in the air, even in a bright room. A screen with a diffusion rate of less than 15% in some ranges within the -10° to +10° range, particularly at -10° and/or +10°, tends to make the real image formed in the air difficult to see in a bright room. A screen with a diffusion rate of 78% or more in this range of -10° to +10° can provide a clear view of the real image formed in the air, even if its transmittance is 65% or more.
From these measurement results, it can be seen that Japanese paper or nonwoven fabric is preferable for the screens shown in Figures 1 to 9, and in particular, those with a basis weight of 11 to 24 g/m ² can be suitably used as screens. Specific examples include tissue paper (machine-made Japanese paper: basis weight 15 g/m ² ), Tengu-hashi paper (basis weight 18 g/m ² ) manufactured by Hidaka Co., Ltd., and Usu Mino 3 momme (basis weight 20.42 g/m ² ).

While the aerial projection devices described above form a real image in the air, they may also be configured so that only a virtual image is visible in the air, as shown in Figure 11. The aerial projection device shown in Figure 11 comprises a holographic projector unit 10a in which parallel light is irradiated onto a hologram created so that each of a plurality of predetermined images is projected at a different predetermined position, and diffracted light diffracted based on the interference information of this hologram is emitted; a second half mirror 30 that is installed at an angle to the irradiated diffracted light and through which the diffracted light is irradiated; and multiple retroreflective sheets 32a, 32b as retroreflective elements arranged without overlapping each other, positioned a predetermined distance from one side of the second half mirror 30 and at predetermined positions where the diffracted light that has passed through the second half mirror 30 is irradiated and projected images corresponding to each of the predetermined images are projected. and a projection unit 10b consisting of the retroreflective sheets 32a, 32b, the retroreflective light emission surfaces of which are arranged facing one side of the half mirror 30 so that the retroreflective light of the projected image emitted from the retroreflective light emission surfaces is reflected by the second half mirror 30 and can be seen as a virtual image in the air on the other side of the second half mirror 30, and at least one of the retroreflective sheets 32a, 32b is arranged to be movably positioned at the projection position of the corresponding predetermined image, or all of the retroreflective sheets 32a, 32b or each of the remaining retroreflective sheets excluding the movably positioned retroreflective sheet is arranged at the projection position of the corresponding predetermined image.

The holographic projector unit 10a shown in Figure 11 is composed of a personal computer (PC) 12 to which a tablet terminal device 11 is connected, a reflective spatial light modulator (SLM) 14, a first half mirror 22, and a parallel light emitting unit 15. The parallel light emitting unit 15 is composed of a laser light emitting unit 16, an objective lens 18, and a plano-convex lens 20. In the holographic projector unit 10a, a computer-generated hologram (CGH) of a predetermined image such as a character or figure input from the tablet terminal device 11 is calculated by the CGH calculation unit 17 of the PC 12 and displayed on the SLM 14. The interference fringes displayed on the SLM 14 are interference information created so that the predetermined image is focused at a predetermined position. Parallel light is irradiated onto the display surface of the SLM 14 on which such interference fringes are displayed. This parallel light is laser light emitted from laser light emitting unit 16 of parallel light emitting unit 15, which is first focused by objective lens 18 and then spreads, becomes parallel light by plano-convex lens 20, and is reflected by first half mirror 22 toward the display surface of SLM 14. The parallel light irradiated onto the display surface of SLM 14 becomes diffracted light based on the interference information of the hologram displayed on the display surface, emerges from the display surface of SLM 14, passes through first half mirror 22, and is emitted to projection unit 10b.

Projection unit 10b is composed of a mirror 24 tilted at a 45° angle, a second half mirror 30 also installed at a 45° angle, and retroreflective sheets 32a and 32b as retroreflective elements located on one side (inclined surface side) of second half mirror 30. Retroreflective sheet 32a is located on the lower end side of the inclined surface of second half mirror 30, and retroreflective sheet 32b is located on the upper end side of the inclined surface of second half mirror 30. Retroreflective sheets 32a and 32b are arranged without overlapping each other, and both retroreflective light exit surfaces face one side of second half mirror 30, which also serves as the projection surface for the predetermined image for which CGH calculation is performed by CGH calculation unit 17 of PC 12. The diffracted light incident on the projection unit 10b from the holographic projector unit 10a is reflected by the mirror 24, passes through the second half mirror 30, and illuminates the retroreflected light exit surfaces of the retroreflecting sheets 32a and 32b. A projection image a is projected onto the retroreflected light exit surface of the retroreflecting sheet 32a illuminated with the diffracted light. From the retroreflected light exit surface of the retroreflecting sheet 32a onto which the projection image a is projected, retroreflected light is emitted in the opposite direction to the incident light of the projection image a. This retroreflected light is reflected by one side of the second half mirror 30 and enters the human eye, and a virtual image a corresponding to the projection image a can be seen in the air on the other side of the second half mirror 30. The depth from the other surface of the second half mirror 30 to the virtual image a (indicated by Fa' in FIG. 11) is equal to the height from one surface of the second half mirror 30 to the retroreflective sheet 32a (indicated by Fa in FIG. 11). Furthermore, a projected image b is projected onto the retroreflective light exit surface of the retroreflective sheet 32b irradiated with diffracted light. From the retroreflective light exit surface of the retroreflective sheet 32b onto which the projected image b is projected, retroreflective light is emitted in the opposite direction to the incident light of the projected image b. This retroreflective light is reflected by one surface of the second half mirror 30 and enters the human eye, and a virtual image b corresponding to the projected image b can be seen on the other surface of the second half mirror 30, further back than the virtual image a. The depth from the other surface of the second half mirror 30 to the virtual image b (shown as Fb' in FIG. 11) is also equal to the height from one surface of the second half mirror 30 to the retroreflective sheet 32b (shown as Fb in FIG. 11). In this way, when viewed from one surface of the second half mirror 30, the retroreflective sheets 32a, 32b as retroreflective elements are arranged at projection positions corresponding to each of the predetermined images so that all of the virtual images corresponding to the plurality of predetermined images can be seen simultaneously, and therefore clear virtual images a, b for the plurality of predetermined images can be seen simultaneously.

Fa, the height from one side of the second half mirror 30 to the projection surface of the retroreflective sheet 32a, is longer than Fb, the height from one side of the second half mirror 30 to the retroreflective sheet 32b. However, virtual image b can be seen further back than virtual image a because the retroreflective sheet 32a is positioned on the lower end side of the inclined surface of the second half mirror 30. In this way, the heights Fa and Fb from one side of the second half mirror 30 corresponding to virtual image a and virtual image b to the retroreflective sheets 32a and 32b as retroreflective elements are adjusted so that virtual image a and virtual image b appear in different positions from the other side of the second half mirror 30. This allows clear virtual images of multiple predetermined images to be seen in different positions at the same time.

Figure 12 shows the state in which the letter "A" is projected as projected image a from the holographic projector unit 10a (see Figure 11) onto the projection surface (hereinafter simply referred to as the projection surface), which is the retroreflected light exit surface of the retroreflecting sheet 32a, and the letter "B" is projected as projected image b onto the projection surface (hereinafter simply referred to as the projection surface), which is the retroreflected light exit surface of the retroreflecting sheet 32b. The letter "A" projected onto the retroreflecting sheet 32a is visible as virtual image a on the other side of the second half mirror 30, and the letter "B" projected onto the projection surface of the retroreflecting sheet 32b is visible as virtual image b on the other side of the second half mirror 30, further back than the letter "A" in virtual image a. In this way, with one holographic projector unit 10a, clear virtual images of the letters "A" and "B" at different distances can be simultaneously viewed from one side of the second half mirror 30 to the other side of the second half mirror 30.

Here, when a mirror was placed in place of the retroreflective sheets 32a and 32b in Figure 11, virtual images a and b were not visible. This is presumably due to the difference in reflection between the mirror and the retroreflective sheet. Furthermore, when white or black paper was placed in place of the retroreflective sheets 32a and 32b, virtual images a and b were visible but were significantly unclear. This is presumably due to the fact that the reflectivity of white or black paper in the retroreflective direction is lower than that of the retroreflective sheet.

Even if a light-shielding plate 31 is inserted between virtual image a and virtual image b shown in Figure 11 as shown in Figure 13, virtual image b can be viewed through the light-shielding plate 31. Furthermore, as shown in Figure 14, by moving the retroreflective sheet 32b in the direction of arrow f (towards the second half mirror 30) to position 32b', the position at which virtual image b is visible can be moved in the direction of arrow f' (towards the second half mirror 30), to position b' in front of virtual image a. However, when moving the retroreflective sheet 32b, a computer-generated hologram (CGH) projecting image b at position 32b' shown in Figure 14 must be calculated by the CGH calculation unit 17 of the PC 12 and displayed on the SLM 14.

As shown in Figures 11 to 14, the position at which virtual images a and b are visible corresponds to the distance (optical path length) between the retroreflective sheets 32a and 32b and the second half mirror 30; the longer the distance (optical path length) between the retroreflective sheet and the second half mirror 30, the further back the virtual image can be seen from the second half mirror 30. If it is desired to increase the distance (optical path length) between the retroreflective sheet and the second half mirror 30 and there are physical constraints such as the size of the room, a mirror 35 can be installed between the retroreflective sheet 32a and the second half mirror 30 as shown in Figure 15 to bend the optical path between the retroreflective sheet 32a and the second half mirror 30 and increase the optical path length.

In the projection unit 10b shown in Figures 11 to 15, two retroreflective sheets are arranged, but as in the projection unit 10b shown in Figure 16, only one movable retroreflective sheet 32a may be used. Diffracted light is emitted from the holographic projector unit 10a to project projected images a and b at predetermined positions on one side (inclined surface) of the second half mirror 30. Therefore, at the position of the retroreflective sheet 32a shown in Figure 16, projected image a is projected and virtual image a can be seen on the other side of the second half mirror 30. If the retroreflective sheet 32a, which is at the projection position of projected image a, is moved to projection position 32a' where projected image b is projected, virtual image a disappears, but projected image b is projected onto the retroreflective sheet 32a, and virtual image b can be seen on the other side of the second half mirror 30. Virtual image b can be seen further back than virtual image a. By moving the movably provided retroreflective sheet 32a to the position where the projected image b is projected, the virtual image b, which has a different perspective from the virtual image a, can be visually recognized.

In the projection unit 10b shown in Figures 11 to 16, the retroreflective sheets 32a, 32b are arranged in series at the top and bottom of the second half mirror 30 as shown in Figure 12. However, the positions of the virtual images a, b are also affected by the tilt of the second half mirror 30. To avoid the effects of the tilt of the second half mirror 30, it is preferable to arrange the retroreflective sheets 32a, 32b in parallel to the left and right of the rectangular second half mirror 30 as shown in Figure 17(a). By arranging the retroreflective sheets 32a, 32b in this way, it is possible to predict that the virtual images a, b will be visible at positions corresponding to the distance (optical path length) of each of the retroreflective sheets 32a, 32b from the second half mirror 30, as shown in Figure 17(b).

In the aerial projection device 10 described above, diffracted light is emitted from the holographic projector unit 10a so that a predetermined image is projected at the projection position (focal position) of the CGH. Accurately knowing the focal position of this CGH is necessary to obtain a clear real or virtual image, or a real or virtual image with a desired blurred shape. The focal position of the CGH can be accurately determined by a guide device that guides the projection target to a predetermined spatial position. This guide device includes a hologram on which an interference pattern is formed, adjusted so that an image of a predetermined shape with a narrow gap pattern is formed at the predetermined spatial position, and a parallel light emission means that emits parallel light toward the hologram so that, when the projection target is guided to the predetermined spatial position, the diffracted light irradiated onto the hologram is diffracted based on the interference pattern, and the pattern formed on the projection target coincides with the image pattern. The guiding method using this guide device uses a holographic projector whose imaging position is adjusted so that an image of a predetermined shape having a narrow gap pattern is projected at a predetermined spatial position, and when an image is projected from the holographic projector onto a projection object placed near this spatial position, the projection object is guided to a spatial position where the pattern of the image reflected on the projection object matches the pattern of the image.

This guide device and guide method will be described in detail using Figure 18. The guide device 70 shown in Figure 18 is composed of a holographic projector unit 10a and a three-dimensional screen 28 as a projection target, slidably mounted on a mounting base 75 in the direction of arrow F. The holographic projector unit 10a is composed of a personal computer (PC) 12 to which a tablet terminal device 11 is connected, a reflective spatial light modulator (SLM) 14, a half mirror 22, and a parallel light emitter 15. The parallel light emitter 15 is composed of a laser light emitter 16, an objective lens 18, and a plano-convex lens 20. In the holographic projector unit 10a, a computer-generated hologram (CGH) of a cube having a narrow gap pattern is calculated by a CGH calculation unit 17 of the PC 12 as a predetermined image input from the tablet terminal device 11, and is displayed on the SLM 14. The hologram interference fringes displayed on the SLM 14 are interference information in which the projection position (focal position) is calculated so that a cube as a predetermined image is projected at a predetermined spatial position. Parallel light is irradiated onto the display surface of the SLM 14 on which such interference fringes are displayed. This parallel light is generated when laser light emitted from the laser light emitting unit 16 of the parallel light emitting unit 15 is first focused by the objective lens 18, then spreads, becomes parallel light by the plano-convex lens 20, and is reflected toward the display surface of the SLM 14 by the half mirror 22. The parallel light irradiated onto the display surface of the SLM 14 is diffracted based on the interference information of the hologram displayed on the display surface, emerges from the display surface of the SLM 14, passes through the half mirror 22, and is projected onto the 3D screen 28.

The 3D screen 28 is cubic in shape as shown in Figure 18(a) and is formed by attaching a white sheet to a frame. This three-dimensional screen 28 is supported via support rods 73 on a support base 74 that is placed on a mounting base 75 so that it can slide in the direction of arrow F, and is rotatable horizontally as indicated by arrow F' and vertically as indicated by arrow F". The three-dimensional screen 28 on the support base 74 shown in Figure 18(a) is adjusted so that two of its side faces serve as projection surfaces onto which diffracted light emitted from the holographic projector unit 10a is irradiated and images of the corresponding two faces of the cube are projected. An image of a cube having a pattern of narrow gaps is projected from the holographic projector unit 10a located on the left side of the projection surface of the three-dimensional screen 28 thus slidably placed on the mounting base 75. This image is input from the tablet terminal device 11, and when the pattern of the input image matches the pattern projected onto the three-dimensional screen 28, it can be seen that the three-dimensional screen 28 is located at the projection position (focal position) of the holographic projector unit 10a.

The pattern of this narrow gap is preferably a pattern consisting of multiple thin lines and dots spaced at a predetermined interval, such as a dotted line pattern 76 projected across the entire projection surface of the three-dimensional screen 28 located at the projection position (focal position) of the holographic projector unit 10a (where the corners of the three-dimensional screen 28 shown in Figures 18(a) and 18(b) are A, B, B', A', C', and C, the surface bounded by sides A-B, B-B', B'-A', A'-C', C'-C, and C-A), in which multiple thin, straight dotted lines are formed with narrow gaps, as shown in Figure 18(b). As shown in Figure 18(a), when the three-dimensional screen 28 is placed on the mounting base 75 with its side A-A' closest to the holographic projector unit 10a, diffracted light from the holographic projector unit 10a is irradiated onto the white sheet projection surface of the three-dimensional screen 28, forming a dotted pattern 76. When the projection surface of the three-dimensional screen 28 is viewed from the direction of the diffracted light, as shown in Figure 18(b), if the thin, straight dotted lines constituting the dotted pattern 76 are clearly distinguishable across the entire projection surface of the three-dimensional screen 28, it can be determined that the three-dimensional screen 28 is located at the projection position (focal position) of the holographic projector unit 10a. On the other hand, when the three-dimensional screen 28 is located farther away from the projection position (focal position) of the holographic projector unit 10a, a slanted line pattern 77 different from the dotted line pattern 76 in Figure 18(b) can be seen when the projection surface of the three-dimensional screen 28 is viewed from the direction of the diffracted light, as shown in Figure 18(c). Furthermore, even when the three-dimensional screen 28 is positioned closer to the holographic projector unit 10a than the projection position (focal position) of the holographic projector unit 10a, when the projection surface of the three-dimensional screen 28 is viewed from the projection direction of the diffracted light, a slanted line pattern 77 different from the dotted line pattern 76 in Fig. 18(b) can be seen, as shown in Fig. 18(c). In this way, the dotted line pattern 76 projected onto the projection surface of the three-dimensional screen 28 makes it easy to determine whether the three-dimensional screen 28 is positioned at the projection position (focal position), and the three-dimensional screen 28 can be slid to guide it to the projection position (focal position).

When projecting a predetermined image onto a flat screen 36 as shown in FIG. 3 or retroreflective sheets 32a and 32b as shown in FIG. 11, it is preferable to use a pattern of narrow gaps, such as a dotted line pattern 78 formed by multiple thin dotted lines spaced apart, as shown in FIG. 19(a). When the thin, straight dotted lines that make up the dotted line pattern 78 are clearly discernible across the entire projection surface of the screen 36 or retroreflective sheet 32 as shown in FIG. 19(a), it is clear that the screen 36 or retroreflective sheet 32 is positioned at the projection position (focal position) of the holographic projector unit 10a. On the other hand, when a slanted line pattern 79 different from the dotted line pattern 78 in FIG. 19(a) is visible, it is clear that the screen 36 or retroreflective sheet 32 is positioned away from the projection position (focal position) of the holographic projector unit 10a, as shown in FIG. 19(b). Therefore, by moving the screen 36 or the retroreflective sheet 32 to a position where the dotted line pattern 78 shown in FIG. 19(a) is formed, it can be accurately set at the projection position (focal position) of the holographic projector unit 10a.

The guide device 70 shown in FIG. 18 can be used in a personal authentication device, for example, a personal authentication device using the iris of a human eye, as shown in FIG. 20. The device shown in FIG. 20 is used to determine the position of a subject in an iris-based personal authentication device. In the position determination device shown in FIG. 20, an image having a narrow gap pattern is projected onto the subject's forehead from a holographic projector unit 10a. The image projected onto the subject's forehead is captured by a camera 80 and displayed on a display device 82 so that the subject can view it. When the image projected onto the subject's forehead matches the pattern of the image input from the tablet terminal device 11, the subject's eyes are within the depth range of the iris imaging camera (not shown). This image having a narrow gap pattern may be a narrow gap pattern, such as a dotted line pattern 78 formed by multiple thin dotted lines spaced apart, as shown in FIG. 19(a). When the pattern projected onto the subject's forehead, photographed by camera 80, and displayed on display device 82 is dotted line pattern 78 as shown in Fig. 19(a), the subject's eyes are within the depth range of the iris photographing camera (not shown) of the personal authentication device, and the subject's iris can be photographed by the iris photographing camera. On the other hand, when the pattern displayed on display device 82 is slanted line pattern 79 as shown in Fig. 19(b), the subject's iris is not located within the depth range of the face iris photographing camera, and the subject moves their face to a position where the pattern displayed on display device 82 becomes dotted line pattern 78 as shown in Fig. 19(a). Note that when dotted line pattern 78 is projected onto the subject's forehead from holographic projector unit 10a as shown in Fig. 20, if there is a risk that diffracted light from SLM 14 may enter the subject's eyes, SLM 14 may be illuminated with light from a light-emitting diode (LED) or infrared light that is not visible to humans but can be recognized by camera 80.

The guide device 70 shown in FIG. 18 can also be used in a personal authentication device using hand veins, as shown in FIG. 21. The device shown in FIG. 21 is used to determine the position of a subject's hand in a personal authentication device using hand veins. In the positioning device shown in FIG. 21, when the subject holds out their hand over the vein imaging camera 84, an image having a narrow gap pattern is projected onto the arm from the holographic projector unit 10a. The image projected onto the subject's arm can be viewed directly by the subject, and when the image matches the pattern of the image input from the tablet terminal device 11, the subject's hand is within the depth range of the vein imaging camera 84. This image having a narrow gap pattern may be a narrow gap pattern, such as a dotted line pattern 78 formed by multiple thin lines spaced apart, as shown in FIG. 19(a). When the pattern projected onto the subject's arm becomes a slanted line pattern 79 as shown in Figure 19(b) and does not match the dotted line pattern 78, the subject's hand is not located within the depth range of the vein imaging camera 84, and the subject moves their hand and arm up or down to a position where the pattern displayed on their arm becomes the dotted line pattern 78 as shown in Figure 19(a). Note that in the device shown in Figure 21, there is no risk of diffracted light from the SLM 14 entering the subject's eyes, and laser light may be irradiated onto the SLM 14 to make the pattern projected onto the arm clearer.

In the aerial projection device 10 described above, a computer-generated hologram (CGH) of a predetermined image input from the tablet terminal device 11 to the PC 12 is calculated by the CGH calculation unit 17 and output to the SLM 14. The computer-generated hologram (CGH) calculated by the CGH calculation unit 17 will now be described. When each object point of the three-dimensional object shown in FIG. 22 is a point light source, the computer-generated hologram (hereinafter simply referred to as CGH) of the three-dimensional object composed of N object points has the light intensity I _comp (x _h , y _h , 0) at each point (x _h , y _h , 0) on the CGH shown in FIG. 22 expressed by the following equation (3):
It can be expressed as:

Incidentally, there are SLMs 14 that display amplitude holograms and SLMs 14 that display phase holograms. As shown in Figure 22, if the position coordinates of the nth point light source on a three-dimensional object are P( _xn , _yn , _zn ), its brightness is _An , the size of one pixel is _Δx × _Δy, and the coordinates of the CGH pixel located at the i-th and j-th positions in the x and y directions are ( _xh , _yh ) = ( _iΔx , _jΔy ), the light intensity _Iamp ( _xh , _yh , 0) at each point ( _xh , _yh , 0) on the amplitude hologram can be calculated by the following formula (4):
It can be expressed as:

Furthermore, the phase I _phase (x _h , y _h , 0) at each point (x _h , y _h , 0) on the phase hologram is expressed by the following formula (5):
It can be expressed as:
In the above formula (5), Im{I _comp } is the imaginary part, and Re{I _comp } is the real part.
Therefore, the above formula (3) can be expressed as the following formula (6):
It can be expressed as:

An amplitude hologram can be calculated based on the above formula (4), and a phase hologram can be calculated based on the above formula (6), and these can be used for calculating CGHs of three-dimensional still images.
However, in the case of three-dimensional video, a further improvement in calculation speed is required compared to the calculation of CGH using the above formula (4) or the above formula (6). Therefore, in order to improve the calculation speed of CGH, the above formula (4) representing the light intensity (I _amp (x _h , y _h , 0)) of the amplitude hologram is changed to the following formula (7):
It was transformed as follows.
Furthermore, the above-mentioned formula (6) representing the phase of the phase hologram (I _phase (x _h , y _h , 0)) is expressed as the following formula (8):
It was transformed as follows.

In order to calculate an amplitude hologram based on the above formula (7) in the CGH calculation unit 17 of the PC 12 of the aerial projection device 10, as shown in FIG. 23 , the CGH calculation unit 17 includes a position coordinate data storage unit 17a that stores data on the position coordinates of the point light source of the three-dimensional image input from the tablet terminal device 11, a CGH x-direction trigonometric function table 17b that stores values obtained by calculating sinX and cosX in the x-direction of the CGH based on the position coordinate data of the position coordinate data storage unit 17a, a CGH y-direction trigonometric function table 17c that stores values obtained by calculating sinY and cosY in the y-direction of the CGH based on the position coordinate data of the position coordinate data storage unit 17a, an amplitude hologram calculation unit 17d that calculates the light intensity (I _{amp (x h , y h , 0)) of the amplitude hologram using the trigonometric function values stored in the trigonometric function tables 17b and 17c, and a light intensity (I amp (} x _h , y _h , 0)) of the amplitude hologram calculated by the amplitude hologram calculation unit _17d . _h , 0) and outputs it to the SLM 14.

The pseudocode for calculating an amplitude hologram in the CGH calculation unit 17 shown in Fig. 23 is shown in Fig. 24, and its flowchart is shown in Fig. 25. The pseudocode shown in Fig. 24 assumes that the resolution of the CGH is W × H, and the flowchart shown in Fig. 25 is for a three-dimensional moving image, but it can also be applied to a three-dimensional still image.
24 and 25, trigonometric function table 17b is created before trigonometric function table 17c, but trigonometric function table 17b may be created before trigonometric function table 17c, or trigonometric function tables 17b and 17c may be created in parallel. Furthermore, the creation of trigonometric function tables 17b and 17c, the calculation of the amplitude hologram by amplitude hologram calculation unit 17d, and the output of the amplitude hologram by amplitude hologram data storage unit 17e to SLM 14 may be processed in parallel. Furthermore, if trigonometric function tables 17b and 17c are created in advance for each frame of a three-dimensional video and can be used to create and display an amplitude hologram to be displayed on SLM 14, the point light source loop may be the innermost loop in the flowchart shown in FIG.

In order to calculate a phase hologram based on the above formula (8) in the CGH calculation unit 17 of the PC 12, as shown in FIG. 26, the CGH calculation unit 17 includes a position coordinate data storage unit 17a that stores position coordinate data of a point light source of a three-dimensional image input from the tablet terminal device 11, a trigonometric function table 17b for the x direction of the CGH that stores values obtained by calculating sinX and cosX in the x direction of the CGH based on the position coordinate data of the position coordinate data storage unit 17a, and a trigonometric function table 17c for the y direction of the CGH that stores values obtained by calculating sinX and cosX in the y direction of the CGH based on the position coordinate data of the position coordinate data storage unit 17a. the phase hologram calculation unit 17h that calculates the phase of the phase hologram (Iphase(xh, yh, 0)) using the imaginary part Im{Icomp} and real part Re{Icomp} calculated by the imaginary part/real part calculation unit 17f and the imaginary part/real part storage unit 17g of the imaginary part Im{Icomp} and real part Re{Icomp} calculated by the imaginary part/real part calculation unit 17f and the imaginary part Im{Icomp} and real part Re{Icomp} stored in the imaginary part/real part storage unit 17g; and the phase hologram data storage unit 17i that stores the phase of _the phase hologram ( _Iphase ( _xh , _yh , 0)) calculated by the phase hologram calculation unit 17h and outputs it to the _{SLM 14} .

The pseudocode for calculating a phase hologram in the CGH calculation unit 17 shown in Fig. 26 is shown in Fig. 27, and its flowchart is shown in Fig. 28. The pseudocode shown in Fig. 27 assumes that the CGH resolution is W × H, and the flowchart shown in Fig. 28 is for a three-dimensional moving image, but it can also be applied to a three-dimensional still image.
27 and 28, trigonometric function table 17b is created before trigonometric function table 17c, but trigonometric function table 17b may be created before trigonometric function table 17c, or trigonometric function tables 17b and 17c may be created in parallel. Furthermore, the creation of trigonometric function tables 17b and 17c, the calculation of imaginary part Im{Icomp} and real part Re{Icomp} by imaginary/real part calculation unit 17f, the calculation of the phase hologram phase ( _Iphase ( _xh , _yh , 0)) by phase hologram calculation unit 17h, and the output of the phase hologram to SLM 14 by phase hologram data storage unit 17i may be processed in parallel. Furthermore, if trigonometric function tables 17b and 17c are created in advance for each frame of a 3D video and a phase hologram to be displayed on SLM 14 can be created and displayed using these tables, the point light source loop may be the innermost loop in the flowchart shown in FIG.

A CGH calculation unit 17 that calculates and processes an amplitude hologram based on the above formula (7) or a phase hologram based on the above formula (8) can be provided within a CPU (Central Processing Unit) and/or a GPU (Graphics Processing Unit).
Both CPUs and GPUs have multiple cores, but to achieve real-time playback of 3D video, at least 30 CGH frames must be calculated and played back per second. However, the number of cores a CPU has is significantly fewer than that of a GPU, and the processing speed of the CPU is slow. While it can be used to process 3D still images, it is not suitable for 3D video processing. On the other hand, a GPU has many cores and can be used not only to process 3D still images but also to process 3D video.

The explanation so far has been about the case where there is one projection unit 10b, but multiple projection units may also be installed. Figure 30 shows the case where three projection units 10b shown in Figure 3 are installed. In Figure 30(a), projection units 10b-1, 10b-2, and 10b-3 are arranged in series so that real images are formed on the same side of the second half mirror 30. A flat screen 36 is placed on each frame 26, and diffracted light 1, diffracted light 2, and diffracted light 3 of holograms with different shapes are irradiated onto each screen 36 from the holographic projector unit 10a (not shown) shown in Figure 1(a). On the screen 36 illuminated with diffracted light 1, a circular image 36a-1 shown in FIG. 30(b) is projected. On the screen 36 illuminated with diffracted light 2, a circular image 36a-2 with a smaller diameter than the circular image 36a-1 is projected, as shown in FIG. 30(b). On the screen 36 illuminated with diffracted light 3, a circular image 36a-3 with a smaller diameter than the circular images 36a-1 and 36a-2 is projected, as shown in FIG. 30(b). The circular images 36a-1, 36a-2, and 36a-3 projected onto each screen 36 are formed as real images 38-1, 38-2, and 38-3 in the space on one side of each second half mirror 30. When viewed from the real image 38-1 side, these real images 38-1, 38-2, and 38-3 appear concentric as shown in FIG. 30(c). By arranging multiple projection units 10b in this manner, complex real images can be formed in the air. The diffracted light 1, diffracted light 2, and diffracted light 3 shown in Figure 30 may be emitted from the same holographic projector unit or from different holographic projector units. While Figure 30 uses a flat screen 36, a three-dimensional screen 28, as shown in Figure 1, can be used to view a complex real image formed in the air from multiple angles. While Figure 30 uses three retroreflective sheets 32, a single retroreflective sheet 32 large enough to cover the three second half mirrors 30 may be used.

The frames 26 on which the screens of the three projection units 10b-1, 10b-2, and 10b-3 shown in Figure 30 are mounted are all the same height, but as shown in Figure 31, moving one frame 26 up or down also moves the screen 36 up or down, and the real image formed in the air moves left or right, moving toward or away from the real image of the other units. In Figure 31, the two projection units 10b-1 and 10b-2 shown in Figure 30 are arranged in series so that real images 38-1 and 38-2 are formed in the air on the same side of the second half mirror 30. A flat screen 36 is mounted on each frame 26, and diffracted light 1 and diffracted light 2 of different holograms are irradiated onto each screen 36 from the holographic projector unit 10a (not shown) shown in Figure 1(a), forming real images 38-1 and 38-2 on one side of each second half mirror 30. Here, when the frame 26 of the projection unit 10b-2 is raised to an upper position 26-1 and the projection position (focal position) of the holographic projector unit is aligned with the screen 36-1 that has moved to position 26-1, the formed real image 38-2' moves to the right (in the direction of arrow f-1) of the real image 38-2 and becomes farther away than the real image 38-1 of the projection unit 10b-1. On the other hand, when the frame 26 of the projection unit 10b-2 is lowered to the lower position 26-2 and the projection position (focal position) of the holographic projector unit is aligned with the screen 36-2 that has moved to the position 26-2, the formed real image 38-2" moves to the left of the real image 38-2 (in the direction of the arrow f-2) and approaches the real image 38-1 of the projection unit 10b-1. By moving the frame 26 on which the screens 36 of the multiple projection units 10b are placed in the vertical direction in this way, the real image 38 of the projection unit 10b that has moved in the horizontal direction can approach and separate from the other real images 38, and various movements can be imparted to the real images. In FIG. 31, the screens 36 of the projection units 10b-2 are aligned with the real image 38-1 of the projection unit 10b-1. In the example shown in FIG. 31, only the frame 26 of the projection unit 10b-1 is moved up and down, but by also moving the frame 26 of the projection unit 10b-1 up and down, the real image 38-1 of the projection unit 10b-1 also moves left and right, allowing it to be superimposed on the real image 38-2 of the projection unit 10b-2 or to move the real image 38-1 behind the real image 38-2. Although two retroreflective sheets 32 are used in FIG. 31, a single retroreflective sheet 32 large enough to cover the two second half mirrors 30 may be used. Note that while FIG. 31 illustrates a flat screen 36, a variety of movements can also be imparted to the real image on the three-dimensional screen 28.

In the above explanation, a reflective SLM 14 was used, but a transmissive SLM may also be used. While a predetermined image was input from the tablet terminal device 11 to the PC 12, the predetermined image may also be input directly to the PC 12. Furthermore, a computer-generated hologram calculated by the PC 12 was displayed on the SLM 14, but interference fringes of the hologram may also be printed on film. Furthermore, while laser light was irradiated onto the SLM 14, light from a light-emitting diode (LED) may also be irradiated.

Examples of the present invention are described in detail below, but the scope of the present invention is not limited to these examples.

Example 1
Measure the visible light transmittance and diffusion rate of the screen material.
(Measuring device)
The measurement device shown in Figure 10 was used.
Light source 50: Emits green laser light (wavelength 532 nm) Diameter of hole 58: 2.5 cm
Light meter: Laser power meter (LP1 manufactured by Sanwa Electric Instruments Co., Ltd.)
Distance L: 1m
Distance M: When measuring transmittance: 0 cm
When measuring diffusion rate: 15 cm

(Screen materials)
The screen materials used for the measurements are shown in the following Table 1. All of the screen materials shown in Table 1 were white.

(Transmittance Measurement)
The transmittance of visible light irradiated on the optical axis of each of the screen materials shown in Table 1 was measured. As described above, the measurement was performed by irradiating the hole 58 with parallel green laser light (wavelength 532 nm) emitted from the light source 50 shown in FIG. 10 , and measuring the amount of light received T0 when the hole 58 was not blocked with the screen material using a laser power meter installed at a position where the light-receiving surface 62 abutted against the hole 58 (M = 0 cm). Next, a screen material was attached to block the hole 58, and the amount of light received _T of light transmitted through the hole 58 and the screen material was measured using a laser power meter installed at a position where the light-receiving surface 62 faced the hole 58 (M = 0 cm). The transmittance was calculated as (T/ _T0 ) x 100. The transmittance of each of the screen materials shown in Table 1 is shown in Table 2 below.

(Measurement of Diffusion Rate)
The amount of received light was measured by rotating the light-receiving surface 62 of the laser power meter shown in FIG. 10 by angles between +10° and -10° relative to the optical axis 51. The distance between the light-receiving surface 62 of the laser power meter and the screen material attached to the hole 58 was always maintained at 15 cm (rotation radius of the light-receiving surface 62: 15 cm). The amount of received light measured at a position where the light-receiving surface 62 was rotated by an angle of ±θ relative to the optical axis 51 is the amount of diffused light (T') that passed through the screen material and diffused by an angle of ±θ relative to the optical axis 51. The diffusivity at a position of angle ±θ relative to the optical axis 51 is expressed as the ratio (T'/ _T1 ) of the amount of received light ( _T1 ) measured at an angle of 0° (M = 15 cm). The diffusivities of each of the screen materials shown in Table 1 are shown in Table 2 below.

Example 2
The three-dimensional screen 28 shown in Figure 1(b) was created using the screen materials listed in Table 1, and the letters "Kochi" and a pattern were drawn on it. This three-dimensional screen 28 was placed in a bright room (527 lux (lx)) using the aerial projection device 10 shown in Figure 1(a). The aerial display reflector RF-Ax manufactured by Nippon Carbide Industries Co., Ltd. was used as the retroreflective sheet 32. The distance from the SLM 14 to the three-dimensional screen 28 was 3 m, and the distance M from the top edge of the three-dimensional screen 28 to the midpoint of the second half mirror 30 was 15 cm. Green laser light (wavelength 532 nm) was emitted from the parallel light emitting unit 15.
Furthermore, in a dark room (0.03 lux (lx)) with the room lights turned off and the windows covered with blackout curtains, the images were observed with the naked eye in the same manner as in the bright room. The results are shown in Table 3 below. In Table 3, when the real image 34 was "clearly visible," it was marked with (++), when it was "distinguishable," it was marked with (+), and when it was "poorly visible," it was marked with (±).
The illuminance of the room was measured using an illuminance meter (T-10A (product name)) manufactured by Konica Minolta Japan, Inc.

As is clear from Tables 2 and 3, the screen materials Nos. 5, 9, and 11 have transmittances of less than 47% on the optical axis, and the real image 34 in the air in a bright room is "barely visible" (±). This is because the amount of light transmitted through the three-dimensional screen 28 is reduced.
In contrast, screen materials Nos. 1 to 4, 6 to 8, 10, and 12 to 15 had transmittances of 47% or more on the optical axis, making it possible to see real image 34 in the air even in a bright room. This was because the amount of light transmitted through three-dimensional screen 28 was greater than that of screen materials Nos. 5, 9, and 11. In particular, screen materials Nos. 10, 13, and 15 (tissue paper, Tengu paper (18 g/ ^m² ), and thin Mino 3 momme) had transmittances of 55 to 65% on the optical axis of three-dimensional screen 28 and a diffusion rate of 15% or more over the entire range of -10° to +10° from the optical axis, making it possible to clearly see the characters and pattern of "Kochi" in real image 34 even in a bright room. This is because, when the transmittance and diffusion rate of the three-dimensional screen 28 are both high, the virtual image (corresponding to the virtual image 39 shown in FIG. 5A) created by the specular reflection of the diffused light irradiated onto the retroreflective sheet 32 becomes difficult to see, while the real image 34 becomes easier to see. It is presumed that when the diffusion rate of the three-dimensional screen 28 is high, the diffused light diffused over a wide range from the projection point 29a of the three-dimensional screen 28 shown in FIG. 1A is retroreflected by the retroreflective sheet 32 and concentrated from a wide range to the image point 34a, making it easy to see, while the specular reflected light of the retroreflective sheet 32 spreads, making the virtual image difficult to see.
In contrast, in Nos. 1 to 4, 6 to 8, and 14, a virtual image (corresponding to virtual image 39 shown in FIG. 5( a)) was also visible superimposed on the real image 34, but by tilting the retroreflective sheet 32 as shown in FIG. 5( b), the virtual image could be moved out of the field of view.
In this way, in the three-dimensional screens 28 Nos. 2, 5, 6, 9, 11, and 12, in which the real image 34 was rated as "distinguishable" (+) or "hardly visible" (±) in a bright room (527 lux (lx)), the real image 34 was rated as "clearly visible" (++) in all cases in a dark room (0.03 lux (lx)).

Example 3
In Example 2, the screen materials No. 5 (plain cotton lawn), No. 9 (machine-made paper), and No. 11 (Tengu paper: basis weight 34 g/cm ² ) for which the real image 34 was rated "barely visible" (±) in a bright room (527 lux (lx)), as well as the diffuser materials Nos. 16 to 22 in Table 1, were fabricated into flat screens, and the word "Kochi" (Kochi) was written on the screen to produce screen 36 shown in FIG. 3(a). Using this screen 36, an aerial projection device shown in FIG. 3(a) was used in a bright room (527 lux (lx)) to visually determine whether a real image 38 of the characters "Kochi" could be seen in the air from the front. As a result, as shown in Table 4 below, the real image 38 of the characters "Kochi" was rated "well visible" (++) on all screens.

Example 4
The CGH calculation unit 17 of the PC 12 shown in Figure 1 was installed in a CPU or GPU, and the CGH creation speed due to differences in the calculation formula for the amplitude hologram CGH was measured by changing the number of object points. The results are shown in Table 5 below.
Calculation formula for amplitude hologram: Formula (4) [Pseudocode: Figure 29(a)]
The above formula (7) [pseudocode: Figure 24]
CGH calculation section 17
CPU: Intel Corporation Core™ i7-8700K
GPU: NVIDIA Corporation GeForce RTX™ 3080

As is clear from Table 5, the CGH creation speed using equation (7) is faster than that using equation (4), and the CGH creation speed using a GPU is significantly faster than that using a CPU, so it can be seen that amplitude holograms using equation (7) on a GPU can be applied to three-dimensional video.
Here, when calculating Equation (4) on a CPU, the calculation load of the cos function becomes large. Therefore, to speed up the calculation, a cos table was used in which one period of 0 to 2π was sampled into 256 equal parts, and the range of the sampled cos function, -1 to +1, was set to an 8-bit integer value of -127 to 127. In addition, the Intel C++ compiler classic Version 2021.2.0 (options: -O3 -xCORE-AVX2 -qopenmp) was used as the compiler, and the number of OpenMP threads was set to 12.

Example 5
The CGH calculation unit 17 of the PC 12 shown in Figure 1 was installed in a CPU or GPU, and the CGH creation speed due to differences in the calculation formula for the CGH of a phase hologram was measured by changing the number of object points. The results are shown in Table 6 below.
Calculation formula for phase hologram: Formula (6) [Pseudocode: Figure 29(b)]
The above formula (8) [Pseudocode: Figure 27]
CGH calculation section 17
CPU: Intel Corporation Core™ i7-8700K
GPU: NVIDIA Corporation GeForce RTX™ 3080

As is clear from Table 6, the CGH creation speed using equation (8) is faster than that using equation (6), and the CGH creation speed of the GPU is significantly faster than that of the CPU, so it can be seen that the phase hologram using equation (8) on the GPU can be applied to three-dimensional video.
Here, when calculating Equation (6) on a CPU, the calculation load of the cos and sin functions becomes large. Therefore, the calculation was accelerated by sampling into 256 equal parts in one cycle of 0 to 2π, and using a cos and sin table in which the range of the sampled cos and sin functions, -1 to +1, is an 8-bit integer value of -127 to 127. In addition, the Intel C++ compiler classic Version 2021.2.0 (options: -O3 -xCORE-AVX2 -qopenmp) was used as the compiler, and the number of OpenMP threads was set to 12.

The aerial projection device of the present invention can be used as an aerial projection device that can project images of elevator buttons, etc. in the air, or as an aerial projection device that can project specified images in the air for education, games, etc.

10: Aerial projection device, 10a: Holographic projector unit, 10b, 10b-1, 10b-2, 10b-3: Projection unit, 11: Tablet-type terminal device, 12: Personal computer, 14: Spatial light modulator (SLM), 15: Parallel light emission unit, 16: Laser light emission unit, 17: CGH calculation unit, 17a: Position coordinate data storage unit, 17b, 17c: Trigonometric function table, 17d: Amplitude hologram calculation unit, 17e: Amplitude hologram data storage unit, 17f: Imaginary part/real part calculation unit, 17g: Imaginary part/real part storage unit, 17h: Phase hologram calculation unit, 17i: Phase hologram data storage unit, 18, 52: Objective lens, 20, 54: Plano-convex lens, 2 2: First half mirror, 24, 35: Mirror, 26: Frame, 26', 26-1, 26-2: Position of frame 26, 27, 74: Support base, 28: 3D screen, 28a: Projected image of cube, 28b: Frame, 28c: Japanese paper, 29a, 29b, 37a, 37b, 37a', 37b', 40a, 40b, 40a', 40b': Projection point, 30: Second half mirror, 31: Light shielding plate, 32, 32a, 32b: Retroreflective sheet, 32': Position of retroreflective sheet 32, 32b': Position of retroreflective sheet 32b, 32a': Projection position, 33a: Reflective sheet, 33b: Glass beads, 33c: Transparent resin layer, 34, 38, 38', 38-1, 38-2, 3 8-3, 38-2', 38-2": real image, 34a, 34b, 38a, 38b, 38a', 38b': image points, 36, 36-1, 36-2: screen, 36a, 36a', 36a-1, 36a-2, 36a-3, 40, 40': projected images, 39, 39', 39", 42, 42': virtual images, 39a, 39a': image points 3 Corresponding point of 8a, 39b, 39b': corresponding point of imaging point 38b, 42a, 42b, 42a', 42b': projection point, corresponding points of 40a, 40b, 40a', 40b', 50: light source, 51: optical axis, 56: plate-like body, 58: hole, 60: measurement object, 62: light receiving surface, 62': position, 70: guide device, 73: support rod, 75: mounting table 76, 78: dotted line patterns, 77, 79: inclined line patterns, 80: camera, 82: display device, 84: vein imaging camera, A, B, C, A', B', C': corners of the three-dimensional screen 28, F: sliding direction of the support base 74, F-1, F-2: movement direction of the frame 26, F': rotation direction of the three-dimensional screen 28 in the horizontal plane, Fa, Fb: height, Fa', Fb': depth, L, M: distance, F": rotation direction of the three-dimensional screen 28 in the vertical plane, f: movement direction of the retroreflective sheet 32b, f-1, f-2: movement direction of the real image 38-2, f': movement direction of the virtual image b, b': movement position of the virtual image b, θ: angle, W: number of horizontal pixels of the CGH, H: number of vertical pixels of the CGH, x _h : x-direction position coordinate of a pixel on the hologram, y _h : y-direction position coordinate of a pixel on the hologram, Δ _x : size of the pixel in the x-direction, Δ _y : size of the pixel in the y-direction, P(x _n, yn _, z _n ): position coordinate of the nth object point P of the three-dimensional object

Claims (12)

The present invention is configured with a holographic projector unit that emits diffracted light obtained by diffracting irradiated parallel light based on interference information of a hologram of a predetermined image, a screen onto which the diffracted light is irradiated and the predetermined image is projected, a half mirror that is installed at an angle with respect to the diffracted light irradiated onto the screen at a position onto which transmitted and diffused light of the diffracted light that has passed through the screen and diffused is irradiated, and a projection unit that includes a retroreflection element onto which the transmitted light or reflected light of the half mirror is irradiated,
An aerial projection device characterized in that the transmitted or reflected light of the half mirror of the transmitted diffused light is retroreflected by the retroreflection element and emitted in the opposite direction along the original incident path, and a real image of the specified image is formed in the air on one side of the half mirror by the reflected light reflected by the half mirror or the transmitted light that passes through the half mirror. The aerial projection device described in claim 1, characterized in that the screen is positioned in front of or behind the predetermined position where the real image is projected based on the interference information of the hologram so that the real image appears blurred. The aerial projection device described in claim 1, characterized in that the retroreflective element is tilted so that the virtual image corresponding to the real image visible on the other side of the half mirror is moved out of the field of view due to specular reflection from the retroreflective element. Diffracted light diffracted based on interference information of each hologram of at least two predetermined images is emitted from the holographic projector unit,
The diffracted light based on the interference information of one of the predetermined images is irradiated onto the screen and passes through the half mirror and the retroreflection element to form a real image of one of the predetermined images in the air,
The aerial projection device described in claim 1, characterized in that diffracted light based on the interference information of the other of the specified images passes through the half mirror without being irradiated onto the screen and is irradiated onto the retroreflected light emission surface of the retroreflecting element, thereby projecting the other of the specified images, and the retroreflected light emitted from the retroreflected light emission surface is reflected by the half mirror, making it possible to see a virtual image of the other of the specified images in the air on the side opposite the reflective surface of the half mirror. The aerial projection device described in claim 4, characterized in that the screen and/or the retroreflective element are positioned in front of or behind a predetermined position where the real image and/or the virtual image are projected based on the interference information of the hologram, so that the real image and/or the virtual image appear blurred. An aerial projection device as described in claim 1, characterized in that the screen is a stereoscopic screen. An aerial projection device as described in claim 1 or claim 6, characterized in that the screen is made of Japanese paper or non-woven fabric. The aerial projection device described in claim 1, characterized in that at least two pairs of combinations of the half mirror and the screen are provided, and the two pairs of combinations are installed in series at a predetermined interval so that the real image is formed in the air on the same side of each of the half mirrors. The aerial projection device described in claim 8, characterized in that the screen onto which a projected image corresponding to one of the real images is projected from the holographic projector unit is movable toward and away from the half mirror so that at least one of the real images moves toward and away from the half mirror. The aerial projection device described in claim 1, characterized in that the hologram is a computer-generated hologram and a spatial light modulator is provided that modulates the parallel light into diffracted light based on interference information of the computer-generated hologram. The computer-generated hologram is an amplitude hologram, and the amplitude hologram is expressed by the following formula (1):
11. The aerial projection device according to claim 10, wherein the aerial projection device is calculated based on the following formula: The computer-generated hologram is a phase hologram, and the phase hologram is expressed by the following formula (2):
11. The aerial projection device according to claim 10, wherein the aerial projection device is calculated based on the following formula: