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We have developed a one-unit system, including creating and displaying a hologram for real-time reproduction of a three-dimensional image via electroholography. We have constructed this one-unit system by connecting a special-purpose computer for holography and a special display board with a reflective liquid crystal display as a spatial light modulator. Using this one-unit system, we succeeded in reproducing a three-dimensional image composed of 10,000 points at a speed of 30 frames per second, which is the video rate in NTSC format. In addition, we were able to control a three-dimensional image in real-time using our system.
©2009 Optical Society of America
1. Introduction
Holography is one of the techniques used to reconstruct a three-dimensional (3-D) image. In holography, a 3-D image is recorded on the hologram via light interference and reconstructed from the hologram using light diffraction. In particular, a hologram created by computing is called a computer-generated hologram (CGH) [1]. Electroholography is the technique to reconstruct a 3-D image by displaying a CGH on an acousto-optic modulator (AOM) [2,3] or a spatial light modulator (SLM) as a liquid crystal display (LCD) [4–7], and applications for 3-D displays are anticipated [8].
To reconstruct a 3-D movie in real-time using electroholography, we must compute a CGH at high speed [9], hence the algorithm for high-speed computing of a CGH is being actively studied by many groups [10–12]. Moreover, it has been reported that they succeeded in creating a CGH using a graphics processing unit (GPU) at high speed and realized the real-time reproduction of a 3-D image [13–15]. On the other hand, they achieved a real-time reproduction by way of the image hologram [16], by way of look up Table [17, 18] and by way of phase-added stereogram [19].
We have developed a special-purpose computer for holography known as HORN (HOlographic ReconstructioN). Moreover, we succeeded in creating 30 CGHs in one second, when the size of a CGH was 1,920 × 1,080 and the number of object points 10,000 [20]. At the same time, we have developed a special-purpose display board with an LCD and a controller and small chip for computing [21,22]. Since communication between the HORN-5 board and the special-purpose display board is enabled, and it is also possible to transmit data of a CGH from the HORN-5 board to the special-purpose display board directly by integrating the special-purpose computer and the special-purpose display board. In this study, we succeeded in reconstructing a 3-D image composed of 10,000 points at the video-rate (nearly 30 frames per second) using our system and we report it in the following text.
2. Computer-generated hologram
When the reference light is parallel light and considerable distances exist between a 3-D image and a CGH, the intensity of a CGH is calculated from Eqs. (1), (2) [7,9].
where I(x α ,y α) is the light intensity of the point (x α ,y α) on the hologram, (x j, yj, zj) are the coordinates of the object image, N is the number of the points of the object image, Aj is the amplitude of the object light, λ is the wavelength of the reference light, rα j is the distance between the CGH and the object point, and p is the dot pitch of the display device respectively.Equation (1) shows that the calculation cost of a CGH is proportional to M × N, where M is the size of the CGH. For example, the calculation cost is 5 billion calculations when N is 10,000 and M is 500,000. The computation time with a 3.4-GHz Pentium 4 CPU is about 10 seconds under those circumstances, making it impossible to reconstruct a 3-D image in real-time. Therefore, we use a suitable algorithm for a special-purpose computer [23].
3. One-unit system for real-time holography
3.1 Special-purpose computer and special displaying board for holography
Figure 1 shows the HORN-5 board [20] and the special-purpose display board [21,22]. The HORN-5 board has four Field Programmable Gate Array (FPGA) chips for calculation purposes, within which the calculation unit of a CGH is installed. The intensity of 200 points is computable dynamically in this calculation unit. Moreover, the intensity of 800 points, namely one line of a CGH, is calculated by the four FPGA chips of the HORN-5 board at the same time. The operating frequency of this circuit is 166 MHz. The leftmost FPGA chip has a low voltage differential signaling (LVDS) bus. The throughput of the LVDS bus is about 33 Mbits per second.
Fig. 1 The left side is the special displaying board and the right side is a special-purpose computer for holography.
The special-purpose display board has a high-definition LCD that is CMD8X6D. The size of this LCD is 800 × 600 and its dot pitch is 12 μm. In addition, this board includes an LCD controller, a 64-Mbit memory for the buffer of the intensity data and a LVDS receiver that receives the intensity data of a CGH from the HORN-5 board.
3.2 Real-time reproducing system for holography
Figure 2 shows the block diagram of the one-unit system composed of the HORN-5 board and the special-purpose display board. The red arrow shows the flow of the coordinate data of the 3-D image and the pink arrow shows the flow of the intensity data of a CGH, respectively.
The object data that is transmitted from the peripheral component interconnect (PCI) local bus is computed by the calculation units in four FPGA chips. The intensity data created by the calculation units in FPGA chips is subsequently transmitted to the FPGA chip using the LVDS transceiver. The intensity data is transmitted from the LVDS transceiver to the LVDS receiver when the intensity data of 800 points (1 line) is gathered. Finally, the intensity data of 480,000 points (800 × 600) are displayed on the LCD when these data are gathered in the LCD controller.
Figure 3 shows the data flow of the previous system and the proposed system, and the data flow of HORN-6 system is also included in previous system [24]. The significant difference of the present system and the previous system is that the data flow is unidirectional in the present system. We therefore established a one-unit system in order to reconstruct a 3-D image in real-time without the cost incurred by bidirectional communication. Moreover, we reduced the overall processing time by performing the transmission of a CGH in parallel with the calculation of the CGH.
Fig. 3 Improvement in the data flow. (a) Data flow of previous system. (b) Data flow of proposed system.
Figure 4 shows a block diagram and an overview of the optical system for reconstructing a 3-D image. This optical system features the special-purpose display board constructed with an LCD, an He-Ne laser mounted laser head with a collimator lens, a beam splitter and so on.
Fig. 4 Optical system of the one-unit system. (a) Block diagram of the optical system. (b) Overview of the optical system.
Figure 4 shows a block diagram and an overview of the optical system for reconstructing a 3-D image. This optical system features the special-purpose display board constructed with an LCD, an He-Ne laser mounted laser head with a collimator lens, a beam splitter and so on. A reconstruction image is observed on an output lens, one meter away from the LCD. The viewing angle is about 3 degrees, and the size of the reconstruction image about 3 × 3 × 3 cm.
Moreover, we have developed software for real-time reproducing, which enables the translation, rotation and reconstruction of a 3-D image from another object data by keyboard operations. The specifications of a host personal computer (PC) are shown in Table 1 .
Table 1. Specifications of the host personal computer
4. Results
4.1 Performance of the real-time reproducing system
Figure 5 shows the calculation time of a CGH (Tcalc) and the transmission time from HORN-5 board to the LCD panel (Ttrans). The size of a CGH is 800 × 600 and its calculation time of a CGH increases in proportion to the number of object points. On the other hand, the transmission time of a CGH is always constant. This is because while the calculation cost of a CGH is proportional to M × N, the transmission time is not proportional to N but M when the number of object points increases. The transmission rate of the LVDS bus is about 15 Mbits per second in Fig. 5.
Fig. 5 Computation time and transfer time of a computer-generated hologram when altering the number of object points
Figure 6 shows the frame rate of the real-time reproducing system. The frame rate holds at 34 fps for the object points ≲9,000 and declines for the object points ≳9,000. This is because we reduced the overall processing time by performing the transmission of a CGH in parallel with the calculation of the CGH as discussed in subsection 3.2. Therefore, the calculation time is concealed in the transmission time for the object points ≲9,000, and the calculation time depends on the number of object points for the object points ≳9,000.
In the result, the performance of the real-time reproducing system reached 30 fps when a 3-D image composed of about 10,000 points was reconstructed.
4.2 Reconstruction movies
Figures 7 and 8 show 3-D movies reconstructed by our system. The reference light is a He-Ne laser with a wavelength of 632.8 nm.
A dinosaur is composed of 6,215 points in Fig. 7. And Fig. 6 shows the frame rate of the reconstruction of the dinosaur is 34.5 fps. Earth is composed of 10,061 points in Fig. 8. And Fig. 6 shows the frame rate of the reconstruction of Earth is 32.8 fps. These movie files are recorded by a digital camera at a speed of 30 fps, so it is shown that the reconstructed images move smoothly. Moreover, it is possible to observe the reconstructions from various angles by our system.
5. Conclusion and future research
We constructed a one-unit system, that performed tasks ranging from computing a CGH to displaying the CGH as well as reconstructing a 3-D movie in real-time via the HORN-5 and special-purpose displaying boards. Consequently, we succeeded in reconstructing a 3-D image composed of 10,000 points at a speed of 30 fps.
In future, we will achieve the enlargement and colorization of the reconstruction image. In particular, there have already been reports that the full-color image is reconstructed from only a single LCD panel by the red, blue and green light emitting diodes (LEDs) [25]. However, the FPGA installed on the HORN-5 board has available capacity, hence we will realize the real-time reproducing of the full-color image adding the calculation units and improving the LCD controller on the special-purpose display board.
Acknowledgments
The present research was supported in part by a Grant-in-Aid for JSPS Fellows (21 4148).
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