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A table screen 360-degree holographic display is proposed, with an increased screen size, having an expanded viewing zone over all horizontal directions around the table screen. It consists of a microelectromechanical systems spatial light modulator (MEMS SLM), a magnifying imaging system, and a rotating screen. The MEMS SLM generates hologram patterns at a high frame rate, the magnifying imaging system increases the screen of the MEMS SLM, and the reduced viewing zones are scanned circularly by the rotating screen. The viewing zones are localized to practically realize wavefront reconstruction. An experimental system has been constructed. The generation of 360-degree three-dimensional (3D) images was achieved by scanning 800 reduced and localized viewing zones circularly. The table screen had a diameter of 100 mm, and the frame rate of 3D image generation was 28.4 Hz.
© 2015 Optical Society of America
1. Introduction
Holography is an ideal technology for generating three-dimensional (3D) images because it reconstructs a wavefront emitted from objects [1]. Therefore, the viewer’s eyes can focus on 3D images such that the vergence-accommodation conflict [2], which causes visual fatigue for conventional 3D displays, does not occur [3]. Electronic implementation of holography is necessary for displaying and transmitting 3D images. Since this technique requires ultra-high resolution spatial light modulators (SLMs), only a limited screen size and viewing zone can be produced directly from currently available SLMs. To increase the screen size and the viewing zone, numerous techniques have been developed, such as spatial multiplexing techniques using multiple SLMs [4–7] and time multiplexing techniques using high-speed SLMs [8–10]. In this study, both the screen size and the viewing zone are increased using a time multiplexing technique. In particular, the viewing zone is extended to all horizontal directions around the screen allowing multiple viewers to view 3D images from all directions. Moreover, the proposed technique provides a table screen, which allows viewers to interact with 3D images using their fingers.
Several techniques have been proposed to construct 360-degree holographic displays. Teng et al. [11] proposed the combination of a Fourier-transform holography system and a rotating tilted mirror. With the focal plane of the Fourier-transform lens located at the rotating mirror, the display could be observed over a 360-degree range around the rotating mirror. An observer tracking system was employed to display 3D images to viewers, as the holograms were generated by a liquid-crystal-on-silicon-type SLM with a frame rate of 60 Hz. This limited the number of viewers. The screen had a diameter of 14.1 mm. Sando et al. [12] demonstrated 360-degree 3D image generation using a digital micromirror device (DMD) as a high-speed SLM. The frame rate of this device was 5,000 Hz. A Fourier-transform holography system was also used, and the diameter of the screen was 24.9 mm. Kim et al. [13] proposed a table screen 360-degree holographic display using a rotating tilted mirror and an imaging system that employed an ellipsoid mirror. The imaging system transferred 360-degree 3D images generated by the rotating mirror to a space in order to realize a table screen. They used a Fresnel holography configuration and a DMD. The diameter of the screen was 35.2 mm. They verified the imaging function by the ellipsoid mirror; however, the 360-degree image generation was not achieved.
SeeReal [14, 15] proposed a technique to increase the screen size. There is a trade-off between the screen size and the size of the viewing zone, and so the viewing zone is reduced. This reduced viewing zone is adjusted to the viewer’s eye positions, which are detected by an eye-tracking system. Our research group has also proposed a technique in which the reduced viewing zone is scanned horizontally by a mechanical scanner, and a high-speed SLM is used to rapidly update the hologram patterns [10]. The system was configured with Fresnel holography and a DMD with a frame rate of 13.333 kHz. The screen size was increased to 2.0 in. (50.0 mm), and the viewing zone was widened to 437 mm at a distance of 600 mm from the screen. The technique proposed in this study scans the reduced viewing zone circularly to enable 360-degree 3D image generation. The width of the viewing zone can be reduced to match the pupil diameter of the eye to practically realize wavefront reconstruction.
The use of a rotating tilted mirror [11, 12] is incompatible with a flat screen, and the use of an ellipsoid mirror [13] increases the system volume. The technique proposed in this study rotates an off-axis lens so that a flat screen can be provided. Rotating the off-axis lens is much easier than rotating a tilted mirror so that the screen size can be easily enlarged with the proposed technique than what was previously possible.
We previously constructed a table screen 360-degree super multi-view (SMV) display using a rotating off-axis lens as a table screen [16]. The SMV displays are based on ray reconstruction; the high-speed projectors displayed parallax images viewed from corresponding viewpoints, and incoherent light sources such as light-emitting diodes were used. Because SMV displays need to generate viewpoints at an interval smaller than the pupil diameter of the human eye, a large number of viewpoints were generated using multiple high-speed projectors. Conversely, the holographic displays reported in this study are based on wavefront reconstruction; the projectors display hologram patterns, and coherent light sources such as lasers are used. Moreover, the holographic projectors are required to eliminate the conjugate image and the zero-order diffraction light generated from the hologram patterns to provide only reconstructed wavefronts. The operating principles of the holographic displays are based on the diffraction of light, and thus the system design and parameters are quite different from those of the SMV displays, which are based on geometrical optics.
In this study, a new technique to construct table screen 360-degree holographic displays is proposed where the screen size is increased and the reduced viewing zone is scanned circularly. An experimental system is constructed to verify the proposed technique.
2. Proposed system
In Fig. 1, a schematic diagram of the proposed table screen 360-degree holographic display is given. An SLM based on microelectromechanical systems (MEMS) technology is used, which can operate at a high frame rate. The MEMS SLM is combined with an imaging system with magnification and a rotating screen. The MEMS SLM generates hologram patterns, the magnifying imaging system increases the screen size, and the rotating screen scans the reduced viewing zone circularly.
The magnifying imaging system is shown in Fig. 2. It consists of a projection lens and a screen lens. The rotating screen has a lens function, and for the ease of explanation, an on-axis screen lens is shown. The projection lens images the screen of the MEMS SLM on the screen lens with an increased magnification. Since the pixel pitch increases on the screen, the diffraction angle of light emitted from the screen decreases. The screen lens redirects light inward so that a localized viewing zone is formed, as shown in Fig. 2. Within this localized viewing zone, the entire screen, i.e., the magnified hologram pattern, can be observed. If the width of the localized viewing zone is comparable to the pupil diameter of the eye, wavefront reconstruction can be practically realized [10]. The term “localized viewing zone” is used in this manuscript to distinguish this type of viewing zone from a “non-localized viewing zone,” which is generated without the screen lens and the screen can be partially observed within it. A single-sideband filter is placed on the focal plane of the projection lens, which eliminates the conjugate image component and the zero-order diffraction light [17, 18].
When the lens axis of the screen lens is shifted away from the rotation axis, the viewing zone is generated outside the rotation axis, as shown in Fig. 3. When the screen lens rotates, the viewing zone rotates correspondingly on a circle whose center is located on the rotation axis. The use of an off-axis lens for scanning the viewing zone enables a table screen. The technique of using a rotating off-axis lens was previously used to realize a 360-degree SMV display [16]. The rotating screen also has a vertical diffusing function, which increases the range of the vertical viewing position. However, the generated 3D images have only horizontal parallax.
The proposed technique is described mathematically. The MEMS SLM has a resolution X × Y, a pixel pitch p, and a frame rate fSLM. The magnifying imaging system has a magnification M and converges light at the distance l from the screen lens. The enlarged screen area is given by (MXp) × (MYp). Since the single-sideband filter blocks half of the Fourier-transformed images along a specific direction, the image resolution along this direction is half of that along the perpendicular direction. Therefore, the magnified pixel pitches are given by Mp and 2Mp. Thus, the light diffraction angles are given by λ/Mp and λ/2Mp, where λ is the wavelength of light. The widths of the localized viewing zones are given by λl/Mp and λl/2Mp, as shown in Fig. 4. When the frame rate of the 3D image generation is f3D, the rotation speed of the screen is 60 f3D rpm. The number of hologram patterns generated during one rotation of the screen is given by L = fSLM/f3D. The localized viewing zones should be aligned on the circle with no gap. As the single-sideband filter does not rotate, the length of the short side of the viewing zone must be considered to eliminate the gaps. Therefore, the radius of the circle (R) where the viewing zones are aligned must satisfy the following condition:
The hologram calculation method used for the proposed system is described in Appendix A. Figure 5 depicts the 3D image display area where the entirety of the 3D objects can be observed from all viewing positions. The 3D images can be generated above the table screen as well as below it. The display area decreases at positions further from the screen.
In this study, the system uses Fresnel holography because this configuration is suitable for increasing the screen size. When Fourier-transform holography is used, the zero-order diffraction light converges near the reconstructed images and degrades them. Because our technique localizes the viewing zone, the entire screen can be viewed from the localized viewing zone. When the viewing zone is not localized, the perceived retinal image consists of number of partial images [10]. Therefore, the image quality is better for localized viewing zones than for non-localized viewing zones [11–13].
The 360-degree 3D displays are able to provide different 3D images to different viewers located around the screen. When the viewing zones are localized, it is easy to calculate the hologram patterns because each hologram corresponds to one specific eye and can be directly calculated from one 3D image. When the viewing zones are not localized, the hologram patterns have to be calculated to generate plural 3D images.
3. Experiments
An experimental system was constructed to verify the proposed technique. A reflective screen was used for the ease of construction.
The MEMS SLM was DMD, specifically a DiscoveryTM 4100 (Texas Instruments, Inc.) The resolution was 1,024 × 768, the pixel pitch was 13.68 μm, the screen size was 0.689 in., and the frame rate was 22.727 kHz. A laser diode with a wavelength of 635 nm was used to illuminate the DMD.
In Fig. 6(a), the structure of the rotating screen is shown. It consists of an off-axis Fresnel lens and an aluminum-coated lenticular lens. As a lightweight lens with a large diameter was required for the screen lens, a Fresnel lens was used. The lenticular lens was used as a vertical diffuser, whose flat surface was coated with aluminum. The lenticular lens consisted of a one-dimensional array of cylindrical lenses. The cylindrical lenses were aligned in the direction along the line connecting the lens axis and the rotation axis of the screen lens. The diffusion angle of the lenticular lens, which was the vertical viewing zone angle of the experimental system, was 55°. Fine-pitched lenticular lenses have been used often as vertical diffusers for holographic displays [19]. In Fig. 6(b), the off-axis Fresnel lens is shown. The focal length of the Fresnel lens is 700 mm. Since light passes through the Fresnel lens two times, the effective focal length is 350 mm. The distance between the lens and the rotation axes was 172 mm. A servo motor was used to rotate the screen. A rotary encoder was used to obtain the image updating signals fed to the DMD. To make the frame rate of the 3D image generation approximately 30 Hz, the encoder generated 800 pulses per rotation. Thus, the frame rate of the 3D image generation was 28.4 Hz. The rotation speed of the servo motor was set to 1,704 rpm. The number of holograms generated during one screen rotation was L = 800.
The screen size was 100 mm (3.94 in.), and the image size was 80.0 mm × 60.0 mm, which corresponds to a magnifying imaging system with magnification M = 5.71. The pixel pitch was increased to p = 78.1 μm. The distance between the screen and the reduced viewing zone was l = 715 mm. The widths of the reduced viewing zone were 5.81 and 2.91 mm, which are comparable to the pupil diameter of the eye. From Eq. (1), the radius of the circle where the viewing zones were aligned was set to R = 371 mm.
The focal length of the projection lens was 120 mm, the distance between the projection lens and the screen was 805 mm, and that between the DMD and the projection lens was 141 mm. Thus, the distance between the single-sideband filter and the screen was 685 mm, which determined the distance between the screen and the reduced viewing zone. The lens shift of the screen Fresnel lens mentioned above was determined accordingly.
A photograph of the constructed experimental system is shown in Fig. 7(a). The projection part including the DMD and the rotating screen part are shown in Figs. 7(b) and 7(c), respectively.
Fig. 7 Photographs of experimental system: (a) total system, (b) projection part, and (c) rotating screen part.
The image magnification was measured, and the viewing zone generation was evaluated. A test pattern was displayed by the DMD. The image projected on the screen was captured by a camera located at the localized viewing zone without using a single-sideband filter. We confirmed that the entire screen could be observed within the viewing zone. The image size measured on the screen was 81.0 mm × 60.5 mm, and the image distortion was 1.5%.
The widths of the generated viewing zones were measured. A cooled CCD camera was located at the four positions corresponding to angles 0°, 90°, 180°, and 270°, as indicated in Fig. 4. The measured intensity distributions along the horizontal direction are shown in Fig. 8. The measured full-width at half-maximum values of the intensity distributions are 6.0, 3.5, 6.1, and 3.5 mm for the four positions, respectively. The measured widths are larger than the calculated ones (5.81 and 2.91 mm) because of the aberrations of the off-axis Fresnel lens.
Fig. 8 Graphs of the intensity distributions of localized viewing zones along horizontal direction, as shown in Fig. 8: (a) 0°, (b) 90°, (c) 180°, and (d) 270° (indicated in Fig. 4).
Finally, the generation of 360-degree holographic images was examined. In Fig. 9, the generated 360-degree images captured from the four directions around the table screen are shown. The 3D image shown in Fig. 9(a) consisted of three objects; a circle, “TUAT,” and “3D” were generated at heights of 70, 90, and 110 mm, respectively, above the screen. In Fig. 9(b), the images of two planes generated at heights of 90 and 110 mm above the screen are shown. From these results, the 360-degree images were produced successfully; the 3D images were oriented differently when viewed from different directions. The objects constituting the 3D images had different heights so that the perceived relative distances between the objects changed depending on viewing positions. The generated 3D images had smooth motion parallax because the interval between the viewpoints was small. Multiple viewers could observe the 3D images simultaneously from different directions around the table screen.
Fig. 9 Generated 360-degree holographic images; photographs were captured from four different directions, as indicated in Fig. 4: (a) symbols (Media 1) and (b) two planes (Media 2).
4. Discussion
Although the proposed technique succeeded in generating 360-degree 3D images, the 3D images were distorted when viewers moved vertically. This was because the proposed technique provides 3D images with only horizontal parallax. This problem can be solved by introducing an eye-tracking system and calculating hologram patterns for each detected eye height. Since our technique localizes the viewing zones, it is easy to deliver 3D images having different vertical parallaxes to viewers having different eye heights. When the rotating screen contains the vertical diffuser, the vertical scanning of the viewing zones is not required.
In the reconstructed images, more blur was observed for objects produced further from the screen. Two types of blurring can be considered. One is scan blur, which appears in the scanning direction. While the viewing zone rotates along the circle, the hologram pattern does not change during one frame period of the DMD. The width of the scan blur is given by ρΔθ, where ρ is the radial distance between the 3D point and the rotation axis on the screen and Δθ is the rotation angle corresponding to the one frame period of the DMD. The other is vertical blur. The vertical diffuser contained in the screen diffuses light in the vertical direction. The width of the vertical blur is given by dz/l, where z is the distance between a 3D point and the screen and d is the pupil diameter of the viewer’s eyes. The combination of these two types of blur becomes more apparent at the positions further from the screen. Scan blur can be reduced by modulating the laser to decrease the time when the DMD is illuminated; however, this will decrease the brightness of reconstructed images. Vertical blur can be reduced by removing the vertical diffuser; however, this will reduce the height of the viewing zone so that the observation of 3D images is difficult.
Speckles were observed in the reconstructed images. Speckles could be reduced by using a light source with lower coherence, such as a light-emitting diode. However, a range of wavelengths of the light source causes blur in reconstructed images.
Flicker was also observable in the reconstructed images because the frame rate of the 3D image generation was 28.4 Hz. The direct solution to reduce flicker is to use MEMS SLM with a higher frame rate. Therefore, the development of high-speed MEMS SLMs is important. The other solution would be to decrease the number of viewing zones aligned on the circle by increasing the width of the viewing zones. However, this method decreases the pixel pitch on the screen so that the screen size decreases.
This study experimentally verified the generation of monochromatic 360-degree holographic images. In order to generate color holographic images, two techniques can be utilized. One is the multi-projection technique, i.e., R, G, and B projectors are used. This technique was used for the table screen 360-degree SMV display to generate color SMV images [16]. The projection lens is shifted against the DMD to allow the arrangement of multiple projectors. The other technique is the time-multiplexing technique, i.e., R, G, and B lasers sequentially illuminate a single DMD. In this case, the frame rate of the DMD must be increased. If the frame rate cannot be increased, the screen size must be reduced to decrease the pixel pitch and increase the width of the reduced viewing zones.
5. Conclusion
A holographic display system was proposed, in which 3D images are produced on a table screen and multiple viewers can view 3D images from all 360-degree directions around this screen. The proposed technique was experimentally verified. A DMD having a frame rate of 22,727 Hz was used to generate the hologram patterns. An off-axis Fresnel lens was used as the table screen to scan the viewing zones circularly. The diameter of the screen was increased to 100 mm, and 800 reduced viewing zones were aligned around the circle. The frame rate of the 360-degree 3D image generation was 28.4 Hz. The generated 3D images could be observed by multiple viewers from any direction around the table screen.
Appendix A: Hologram calculation method
The point-based method is used to calculate the hologram patterns; 3D objects are represented by an aggregate of object points. The position of the ith object point is denoted by (Xi, Yi, Zi), its complex amplitude is denoted by Ai, and the total number of the object points is denoted by N. The object wave that is to be reconstructed is given by
where Ci is the constant complex amplitude. The screen lens converges light to the localized viewing zone, whose position is denoted by (xv, yv, zv). Defining θ as the rotation angle of the screen, the position of the light-converging point is given by xv = Rcosθ and yv = Rsinθ, and zv is the height of the viewing position. As the phase modulation of the screen lens is represented by the phase of a spherical wave converging to the light-converging point, the wavefront produced on the screen lens by the hologram projector is given by where C’i is the constant complex amplitude. Comparing Eqs. (A1) and (A2), the positions of the object points are modified to (X’i, Y’i, Z’i) using Eq. (A3) to calculate the hologram pattern. When the single-sideband filter is used to remove the conjugate image and the zero-order diffraction light, the hologram patterns can be calculated by adding the half-zone plates corresponding to the object points [17, 18]. The half-zone plates, whose size and pitch are determined by Z’i, are placed at the position (X’i, Y’i), and the half-zone plates corresponding to all modified object points are added to obtain the hologram patterns.Acknowledgment
The present study was partly supported by the CASIO science promotion foundation, Japan.
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