We demonstrated that placing a pair of prism sheets in front of a display and rotating them overcomes the upper resolution limit of Integral Photograpy (IP) / Integral Videography (IV) imposed by the Nyquist sampling theorem. A pair of prism sheet with the same pitch placed in front of an IP or IV display parallel-shifts the light rays in the 3D space. Rotating the pair shifts the light rays, causing them to appear to rotate around their original positions. Changing the gap between the sheets changes the diameter of the apparent rotation. Changing the speed at which the sheets are rotated changes the speed of the image movement. Experimental results showed that the quality of the IP and IV images is improved by using this technique. It is a simple and effective way to improve the viewing resolution of IP and IV images without reducing their 3D aspects, such as image depth. It also eliminates the need to move the lenslet array.
© 2007 Optical Society of America
Integral photography (IP)  is a method for displaying three-dimensional (3-D) autostereoscopic images that can be formed from an arbitrary viewpoint without the use of supplementary glasses or tracking devices. A number of elemental images with different perspectives for a given 3-D object are generated and recorded on film. When the film is placed at the same position relative to the lens array and is irradiated with a backlight, the light rays retrace their original routes reproducing the image at the same position as that of original object.
IP and relative animated images have attracted much attention in a variety of 3-D image fields. A real-time pickup and 3-D display system based on IP has been developed for 3-D visualization . A gradient-index lens array and a compatible high-definition TV camera have also been developed for IP image pickup to solve the pseudoscopic problem . Igarishi et al. described a method that generates elemental images using a computer process instead of using a physical process. This computer-generated integral photography method can be implemented in both real and virtual IP modes . We previously described integral videography (IV) , which is an animated extension of IP. IV uses a fast image rendering algorithm to project an image of computer-generated graphical object through a micro-convex lens array. Each point shown in a 3-D space is reconstructed at the same position as that of the actual object by the convergence of rays from the pixels of the elemental images on the computer display after they pass through the lenslets in the lens array. Switching to “scene” mode enables IV to display animated objects.
IP/IV images have been shown to accurately reproduce the wavefronts that emanated from original photographed or computer-generated objects. Recent enhancements include widening the viewing angle and enhancing the depth of the IP images [6–8]. Despite IP/IV’s many advantages, the viewing resolution of its spatial images (image quality) is still poor. In addition to aberration and lens deviation, the pixel pitch of the display and the lens pitch are the main factors affecting the IV image format.
A number of researchers have worked on improving the viewing resolution of IP/IV images using defocus and image diffusion to increase the resolution of the target area. For example, one study showed that the mismatch between the image position and focusing position of the lens improves the spatial resolution of required area . The image depth can be enhanced by using time-division multiplexing to adjust the distance between the screen and the lens array for both real and virtual image fields . Another study showed that placing a diffusion sheet in front of the display can smooth the formed image, resulting in higher-quality spatial autostereoscopic image formation . Although the quality of real IP images was improved, the improvement was limited to the area around the diffusion sheet.
Several multiplexing methods have been proposed for increasing the quality of displayed IP images, including space, time, and spatiotemporal multiplexing . However, the increase in quality is limited due to the theoretical binding of the IV image resolution to the pixel density of the display (such as an LCD). We proposed a fundamental principle of multi-projection for increasing both image resolution and pixel density  and developed a two-projector-based display system  for high-resolution IV image display. Furthermore, a relative image calibration and correction technique was developed for creating a seamless multi-projection IV image . Spatial multiplexing by using multiple displays can also increase the viewing and visual zone . Multiple displays combined with masking can be used for increasing the viewing angle .
With time-division multiplexing, the use of a non-stationary lens array can improve the viewing resolution of IP images [17–19]. The synchronously moving lenslet array technique (MALT) is used for image pickup and display in three-dimensional IP imaging. To increase the spatial sampling rate, the positions of the lens array for both pickup and display are rapidly vibrated synchronously in the lateral direction within the retention time of the after-image of the human eye. The image sensor and display are moved together with the lenslet arrays synchronously. The motion speed is typically set to cover at least one pitch within one exposure of the CCD. In this way, the effective aperture of a lenslet is increased synthetically. As a result, the object visual field is increased, and the resolution of the diffraction-limited images is improved. When the MALT is used, the lens array has a periodic structure with a vibration range of less than the pitch of the lens. Computer-generated IP can be implemented using MALT; the elemental images are computationally reconstructed by the MALT-based optical pickup process [20–21]. MALT can thus be used for improving both viewing resolution and image depth.
An open issue is that both the pickup and display devices should be fast enough to represent moving elemental images. With MALT, a driving device is needed for vibrating the lenslet array for each IP pickup and display device. It is difficult to drive a large lenslet array and keep it stable at the same time. The movement of the lenslet array must be synchronized with that of the pickup so that their relative positions are maintained. Moreover, the vibration of the lens array affects the endurance and stability of the device.
We have developed a technique for improving the viewing resolution of the IP/IV image. A pair of prism sheets is placed in front of the display and rotated to overcome the upper resolution limit of IP/IV images imposed by the Nyquist sampling theorem. This technique eliminates the need to move the lenslet array.
2. Materials and Methods
2.1 Rhomboid prism and prism sheets for refracting light rays
Optical prisms are used to refract light and dispersive prisms are used to break light up into its constituent spectral colors because the refractive index depends on frequency. White light is a mixture of rays of different colors, and, when it passes through an optical prism, those of each color are bent slightly differently. For example, the blue light rays are bent more than the red light ones because they are slowed down more.
A rhomboid prism is often used for redirecting the rays without affecting the image composition. Figure 1(a) shows how light rays from a display are parallel-shifted when a rhomboid prism is placed in front of the display. The amount of the shift depends on the incident angle of the rays and the thickness of the prism. If the angle of incidence of the rays on the prism face is smaller than that on the exit face, there is no internal reflection. In short, placing a rhomboid prism in front of an IV display parallel-shifts the light rays from the display, producing the same effect as moving the lens array down [Fig. 1(b)].
2.2 Rhomboid prism converted into double-sided prism sheets
A rhomboid prism can be divided into prismlets [Fig. 2(a)], which can then be used to form a double-faced prism sheet [Fig. 2(b)]. If one of the lateral edges of the prism angle is vertically aligned with the prism plane, all the light rays are shifted in same direction. The total thickness can be made adjustable by separating the double-faced prism sheet into two single-faced prism sheets, as shown in Fig. 2(c). The distance of the shift can be adjusted by adjusting the deflection angle of the prismlets and the distance between the two prism sheets. Light dispersion can be ignored because of the small thickness of the prism sheets. Since the viewing angle of the IP/IV image is limited, light rays passing through the sloped plane from a different direction causes little error. The pair of sheets is rotated relative to the lens array as illustrated in Fig. 2(d).
2.3 Prism sheet rotation
Rotating the prism sheets causes the light rays from the IV display to appear to rotate around their original position; the diameter of the apparent rotation is equal to the distance of the shift. The radius of the apparent circular motion must be smaller than one-half pitch of a lenslet.
Figure 3(a) shows that the rays are shifted downwards when the pair of sheets is in the starting position, i.e. horizontally aligned. Rotating the pair 90° counterclockwise shifts the rays to the right, as shown in Fig. 3(b). Figures 3(c) and 3(d) show the corresponding shifts when the pair is rotated to the 180 and 270° positions. The frequency of the cycle can be controlled by changing the rotation speed.
The concept is illustrated in Fig. 4. Each ray appears to rotate around its original position with a radius corresponding to the shift distance. A pair of prism sheets with the same pitch is placed in front of the display so that all the rays are shifted in parallel and rotated around their original position in the 3D space. This produces the same effect as moving the lens array. We can adjust the gap between the sheets to obtain the optimal shift distance, i.e., rotation diameter. We can adjust the sheet rotation speed to obtain the optimal lenslet array movement, which is captured with a sensor as described in next section.
2.4 Synchronically display element image corresponding to orientation of prism sheets
The element images can be calculated by computer or captured by camera. To reconstruct the IV image, we need to synchronically reproduce the displayed element images corresponding to the orientations of the rotated prism sheets. The system configuration we used for investigating the effects of prism sheet rotation is diagrammed in Fig. 5. We use a photo sensor to capture the rotation situation. A marker is attached to the edge of the prism sheets so that the sensor can achieve the phase difference of the rotation. An oscilloscope (Tektronix, TDS1002B) is used for displaying both of the output voltage and the wave captured by the photo sensor. The oscilloscope changes the calibrated wave signal to the digital signal. Furthermore, the signals corresponding to the rotated prism sheets are transferred to a computer via a USB cable. A program with user interface is developed to analysis the signals and calculate the corresponding rotation cycles of the prism sheets. The elemental images are displayed and updated according to the cycle of the rotation. This method enables the improvement of the image quality without affection of adjusting the distance between the lens array and the display or the captured camera.
3.1 Setup and methods
We fabricated a pair of prism sheets as described above and mounted them in front of an IV display (Fig. 6). The distance between the sheets could be adjusted to match the optical parameters of the lens array. The sheets were made of translucent plastic with a prism angle of 11° and a refracting angle of 5°. The facet spacing was 0.508 mm, and each sheet was 2 mm thick. The gap between them was adjusted by turning the screws connecting them. A 6-V DC motor (MFA, RE-540/1) was used to rotate them. The maximum rotation speed without a load was 7500 rpm.
Each lenslet in the lens array was hexagonal with a base area of 1.016 mm, which covered eight by seven pixels of the displayed image. The element images were calculated by computer.
We estimated the parameter of the prism sheets and the rotation speed on the basis of the IP display specifications. We adjusted the ray shift from 0.1 to 0.5 mm by adjusting the gap between the sheets from 2 to 10 mm.
We also evaluated the maximum spatial resolution of the displayed images by using an IV image with Japanese characters [the lower part in Fig. 7(a)]. The projected images were taken using a digital camera (Nikon D1X, 3008×1536 pixels). The focal length and F-number of the camera lens were 50 mm and 16, respectively. The pupil diameter of the camera iris was about 3 mm, which is similar to that of the human eye in an ordinary lighted indoor environment.
Figure 7(a) shows the original IV image. The shape of each lenslet is clearly evident. Placing the prism sheets in front of the display shifted the image and reduced its brightness slightly, as shown in Fig. 7(b). Figure 7(c) shows the result of rotation. The light rays appear to have been rotated in a circle manner as observed from the front of the display. When the reconstructed image is viewed with the naked eye, one can clearly see the characters without any effects due to the shape of the lenslet. Moreover, the intensity distribution is clearly smoother.
The updating of the element images corresponding to the rotation of the prism sheets was not so good enough for reproducing the IV image with the manufactured prototype device. The quality of the reconstructed image should be much better than shown in the figure by using a precision rotation speed capturing and images synchronic updating device.
Movie of the IV images without and with rotated prism sheets are shown in Fig. 8. Since the IV image was purely three-dimensional, it was difficult to record the image using conventional video recorder. The quality of the actual image was much better than shown in this video.
4. Discussion and summary
The experimental results show that the image quality of IV images can be improved using the proposed technique. This rotated prism sheet technique is a simple and useful way to improve the viewing resolution of IP/IV images without reducing the 3D aspect, such as the image depth, of the reconstructed images.
Color aberration is a common problem when using a prism. Since we used two prism sheets with a small gap between them, we could ignore the light aberration. The IV viewing resolution could be improved by adding a reflection-prevention feature to the prism sheets.
This technique is applicable to real-time pickup and to related 3-D display systems. The IV image depth can be improved by using prism sheets with different prism pitches. Both the viewing resolution and viewing angle could be improved by using the rotating prism sheet technique and a compatible optical design.
We plan to investigate the relationship between the parameters of the prism sheets and the IV image quality. Since the multiple facets structure will degrade the quality of the observed image , the influence factors on the IV image such as the viewing distance and the lenslet’s fill factor should be also considered. Furthermore, the synchronic updating of the element images corresponding to the rotation of the prism sheets should be improved. We thus plan to improve the synchronic display of element images corresponding to the rotation of the prism sheets.
In summary, we have developed a technique that improves the viewing resolution of the integral videography and eliminates the need to move the lenslet array. The combined use of rotated prism sheets and the corresponding captured or calculated element images is a promising approach to overcoming the upper resolution limit of IP/IV images.
This work was supported in part by Grant- in-Aid for Scientific Research (17680037) of the Ministry of Education, Culture, Sports, Science and Technology in Japan and Grant- in-Aid of Strategic Information and Communications R&D Promotion Programme (062103006) of the Ministry of Internal Affairs and Communications in Japan (both to H. Liao).
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