This paper proposes a novel optical system to form an aerial image over a transparent sphere. The proposed optical system is composed of two transparent acrylic spheres in the light path of the aerial imaging by retro-reflection (AIRR) device. The first sphere collects the diverging light rays from a light-source display. The second sphere converges retro-reflected light rays to the aerial image. Raytracing simulation results shows that the area of light entering the retro-reflector can be reduced. Furthermore, this reduction of retro-reflector has been confirmed with a prototype aerial display by the use of a piece of retro-reflector. Thus, the proposed optical system features reduction in the area of expensive retro-reflector.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Three-dimensional (3D) displays have been investigated and developed for a wide variety of applications including advertisement, amusement, and medical tools . In particular, the use of 3D display as a touchless interface is currently attracting attention from the perspective of preventing the spread of infectious diseases. Aerial imaging by retro-reflection (AIRR) [2,3] is one of the prospective techniques to realize a touchless aerial interface. AIRR forms a floating real image in mid-air that is visible by naked eyes. The conventional AIRR device consists of a light source, a beam splitter, and a retro-reflector. Various optical systems on AIRR have been reported: a secure aerial display by use of three-layered liquid-crystal display panels , a 3D aerial display that combines AIRR with depth-fused 3D [5,6], a walk-through aerial display that shows the different images to the three directions , an immersive aerial display surrounding users , and a thin optical system of AIRR by use of faced mirrors . Moreover, AIRR features a wide viewing angle of the aerial image, a large-size scalability aerial image, and a high degree of freedom in optical setups, including a see-it-through function .
In conventional AIRR configuration, the size of retro-reflector is required to be the same as or larger than the light-source display. However, the retro-reflector with good reflective accuracy is expensive. Thus, it is desirable to realize a broad viewing angle of aerial display by the use of retro-reflector with as small area as possible.
In this paper, we propose a method to form an aerial image by installing two transparent acrylic spheres in the light path of AIRR device. Our proposed method allows us to reduce the required area of retro-reflector, without changing the basic configuration of the device and spoiling the appearance of the aerial image. One transparent sphere is placed between the beam splitter and the light source, and the other is placed between the beam splitter and the aerial image. Section 2 shows the principle of our optical system. In Section 3, ray tracing simulations have been performed. In Section 4, a prototype aerial display has been developed and the reduction of the retro-reflector has been confirmed. Sections 4 and 5 are discussion and conclusion of this paper.
We reported preliminary results in Information Photonics 2017  and 24th Microoptics Conference 2019 . In this paper, we have performed ray tracing simulations when there are transparent spheres on the light path to form the aerial image. Furthermore, we have conducted experimental comparisons in the appearance of the aerial image formed with the conventional AIRR and with the proposed method under the limited size of retro-reflectors.
Figure 1(a) shows the diagram of conventional AIRR. This setup consists of a light source, a beam splitter, and a retro-reflector. The beam splitter reflects rays from the light source. The reflected rays are retro-reflected, that is, reflected reversely at the incident positions on the retro-reflector. The retro-reflected rays are converged to the plane-symmetrical position of the light source with respect to the beam splitter.
Figure 1(b) shows the diagram of our proposed method where the two same transparent spheres are placed plane-symmetrically regarding the beam splitter. The light emitted from the light source passes through Transparent sphere 1 with refraction, and then the light is reflected by the beam splitter and enters to the retro-reflector. The retro-reflected light passes through the beam splitter and is refracted by Transparent sphere 2, which forms aerial image at the plane-symmetrical position of the light source with respect to the beam splitter.
Figure 1(c) shows the case where there is one transparent sphere between the light source and the retro-reflector. The retro-reflected light goes ahead without refraction; thus the retro-reflected light does not converge to form an aerial image.
3. Ray tracing simulations
Figure 2 shows the diagram of the optical setup for ray tracing in AIRR with transparent spheres. Ray tracing was performed by use of LightTools 9.0.0. LightTools is one of the major 3D optical design analysis software. The surface light source is a square of 50 mm square and is placed at an angle of 45 degrees to the beam splitter. The wavelength of the light source is 550 nm. The directivity of the surface light source (called the target sphere in LightTools) is 45 degrees. Transparent sphere 1 and the surface light source are touching at the center point of the surface light source. The size of the retro-reflector is 110 mm square, which is enough to receive the light reflected from the surface light source through the transparent sphere to the beam splitter. In this simulation, the retro-reflector has retro-reflection without spreading and attenuation. The shape of the beam splitter is 200-mm square. It has the characteristics of a half-mirror. The two transparent spheres have the same diameter of 70 mm. The spheres are made of polymethyl methacrylate (PMMA). The refractive index of PMMA for the wavelength 550 nm, which is used for experiments, is 1.4936. They were placed symmetrically with respect to the beam splitter and were tangent at the center of the beam splitter. Note that the transparent sphere has chromatic aberration. However, the refraction of light by Transparent sphere 1 is canceled by Transparent sphere 2, so there is no effect of chromatic aberration when the image is formed.
First, we simulated the scattering of light incident on the retro-reflector with and without a transparent sphere. In this simulation, retro-reflectors were replaced by detectors. Figure 3(a) shows the simulation results without a transparent sphere, that is, conventional AIRR, where light rays are emitted from the light source and enter the retro-reflector. Figure 3(b) shows the simulation result of the illuminance distribution in that situation. From this result, it was found that the incident light was distributed in the range of 40 mm to 70 mm in the X axis direction and in the range of about 10 mm to 60 mm in the Y axis direction of the retro-reflector. The light from the light source is widely distributed radially in the direction along the Y-axis. In addition, there is some light rays which has leaked to the outside in the X-axis direction, which suggests that the light from the light source cannot be used enough to form an aerial image.
Figure 4(a) shows the simulation results with a transparent sphere where light rays are emitted from the light source and enter the retro-reflector. Figure 4(b) shows simulation results of the illuminance distribution in that situation. From these results, it was found that the incident light was distributed in the range of 0 mm to 40 mm and 55 mm to 110 mm in the Y axis direction of the retro-reflector. Moreover, the light rays in the X-axis direction was approximately within the expected size of the retro-reflector used in the simulation. The results show that the transparent sphere acts as a ball lens and thus converges the light from the light source.
Next, we performed ray-tracing simulations from the light source through the optical system to the aerial image. The parameters of optical elements are the same as those shown in Fig. 2. The detector is placed at the position of plane-symmetry with the light source and the beam splitter.
Figure 5(a) shows the results of ray tracing simulation of conventional AIRR. Figure 5(b) shows the simulation results of illuminance distribution at the imaging surface of an aerial image. The results show that an aerial image of a 50-mm square is formed in the air. Because the light source is 50-mm square, the results show that aerial image of the same size as the light source is formed.
Figure 6(a) shows the results of ray tracing simulation of AIRR using two transparent spheres arranged in plane-symmetry with a beam splitter. Figure 6(b) shows the simulation results of the illuminance distribution at the imaging surface. It was confirmed that the diverging rays after the retro-reflection were converging again due to the addition of a transparent sphere in the plane symmetry with the beam splitter.
Figure 7(a) shows the results of ray tracing simulation of AIRR using one transparent sphere under the beam splitter. Figure 7(b) shows the simulation results of illuminance distribution at the same imaging surface as in Fig. 5(a) and Fig. 6(a). It was found that the rays of light spread out and light path is distorted due to the loss of Transparent sphere 2.
4. Experiments by use of a prototype aerial display
Figure 8 show the observation results of aerial images using the assembled device. The structure of each device in Figs. 8(a), 8(b) and 8(c) is in accordance with the principle diagram shown in Figs. 1(a), 1(b) and 1(c), respectively. The acrylic sphere is 70 mm in diameter and is placed in contact with the acrylic plate as beam splitter. A smart phone (DoCoMo Galaxy S8.4 SC-03G) is used as a light-source display. A retro-reflector for aerial display (RF-Ax, Nippon Carbide Industries) is used for experiments. This retro-reflector is a prism-type reflective element that reflects incident light in the direction of the angle of incidence by three mutually perpendicular reflective surfaces. The displayed area on the smart phone screen is the 50-mm square area. The displayed image is a green star mark of a size that fits into this 50-mm area. In our proposed method, we were able to observe an aerial image as transparent as the one formed by the conventional AIRR. However, in the case using only one transparent sphere, no aerial image was observed.
4.2 Reduction of retro-reflector
Based on the simulation results in Fig. 4(b), we have conducted an experiment to form aerial images using a retro-reflector that leaves only the area where light rays are concentrated. The structure of device was the same as in the simulation. Figure 9(a) shows the size of the retro-reflector required for conventional AIRR. Figure 9(b) show the size of the retro-reflector cut based on the simulation results. Figure 9(c) is a photograph of the retro-reflectors that we used for experiments.
Figure 10 shows the observation results of aerial images using conventional AIRR with partial retro-reflector. The aerial image was not observed in the area where the retro-reflector was cut off. Furthermore, the narrow area of the retro-reflector limited the viewpoint from which the entire aerial image can be viewed.
Figure 11 shows the observation results of aerial images using proposed method with partial retro-reflector. Figure 11(a) shows that the aerial image is observed without interruption when viewed from the front. Figure 11(b) shows that the viewing angle in the horizontal direction is wider than that in Fig. 10(b). Similarly, Fig. 11(c) shows that the horizontal viewing angle is also wider than Fig. 10(c).
In the proposed method, the shape of the object to be symmetrically placed by the beam splitter is not limited to a sphere. For example, an aerial image can be formed even if the object has a complicated shape, as long as it is placed symmetrically in the beam splitter. However, if the light from the light source is incident on the object, refracted, and reflected by the beam splitter, and cannot reach the retro-reflector, the aerial image will not be formed. For future work, we are considering forming an aerial image with a glass of water or a plastic bottle.
The results of numerical simulation suggested that the transparent sphere used in the proposed method plays the role of a ball lens. By using this, it may be possible to increase the size of the aerial image. In this study, two transparent spheres of the same size were used. By replacing the transparent sphere installed on the beam splitter to larger one than the other sphere under the beam splitter, the aerial image can be expected to expand. In the conventional AIRR configuration, the aerial image is the same size as the light source, and a lens must be installed in the light path to upsize or downsize the aerial image. There is a possibility that the proposed method can realize the enlargement of the aerial image and the saving of the retro-reflector at the same time.
The evaluation of the image quality of the aerial image in the proposed method is the future work. The resolution of the aerial image formed with the conventional AIRR have been evaluated as modulation transfer function (MTF) by a slanted knife edge method . Furthermore, it has been found that the MTF of AIRR by use of a prism-type retro-reflector is anisotropic depending on the angle of the retro-reflector . Thus, image quality evaluation study requires more detailed optical system design for a practical use.
We have performed numerical simulations and observational experiments for AIRR combined with transparent spheres. The numerical simulation results show that the required area of the retro-reflector becomes narrow by placing first transparent sphere between light source and beam splitter. Furthermore, by placing Transparent sphere 2 at the symmetrical position of Transparent sphere 1 with respect to the beam splitter, the aerial image has been successfully formed as in the conventional AIRR. In particular, the area of the retro-reflector through which light passes became smaller than that of the conventional AIRR. It was actually observed that the aerial image was not interrupted even if the retro-reflector was cut off so as to match this simulation result. The appearance of the aerial image from the horizontal and vertical viewpoint were also unaffected by cutting off the retro-reflector. Thus, combining transparent spheres to AIRR enables the reduction of expensive retro-reflector while keeping the visibility of the aerial image, which brings the costs down in an aerial display system.
Accelerated Innovation Research Initiative Turning Top Science and Ideas into High-Impact Values (JPMJAC1601); Japan Society for the Promotion of Science (19H04155, 20H05702, 24300041).
The authors declare no conflicts of interest. This work is original and has not been published elsewhere.
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