A frameless multi-view display module that consists of an array of microelectromechanical system (MEMS) based projectors, a sparse lenticular lens, and a vertical diffuser is proposed to provide a large-screen autostereoscopic display. The projectors are positioned in a horizontal vector form or in a matrix form in front of the transfer screen in order to produce the same number of three-dimensional (3D) pixels in each cylindrical lens constituting the lenticular lens to increase the horizontal resolution of the module. The projectors generate a slanted two-dimensional array of dots on the vertical diffuser to provide a large number of viewpoints. The experimental display system was constructed using four projectors. The system had a 3D resolution of 160 × 120, and it provided 64 views. The screen size was 14.4 in.
©2012 Optical Society of America
Large-screen three-dimensional (3D) displays allow many viewers to observe 3D images simultaneously, and also provide them with realistic impressions. Glasses-type large-screen 3D displays have become popular in movie theaters. However, it is difficult to realize autostereoscopic displays [1–6] with a large screen because a large number of viewpoints, in addition to a large screen, must be generated to allow many viewers to observe 3D images simultaneously.
Autostereoscopic displays having a large screen of, for example, more than 100 inches are generally constructed using multiple projectors. Two types of multi-projection systems can be used: the superposition [7–11] and tiling types [12–14]. The superposition type consists of an array of projectors lined up horizontally and a transfer screen having a lens function, as shown in Fig. 1(a) . All images produced by the projectors are superimposed on the screen, and the screen images the exit pupils of the projection lenses onto the observation space to produce viewpoints for observers. This type requires a long distance between the projectors and screen to increase the screen size. Although this problem could be solved by increasing the magnification of the projectors, the use of high-magnification projection lenses increases the cost. As shown in Fig. 1(b), the tiling type consists of an array of projectors and a light control screen, such as a lenticular lens or parallax barrier. All projectors project images that are tiled on the screen. Although this type requires a shorter distance between the projectors and screen compared to the former type, precise alignment between the projected images and light control screen is required, in addition to precise color matching among all projectors.
In this study, we proposed a multi-view display module using microelectromechanical system (MEMS) projectors. The proposed display system is illustrated in Fig. 2 . The multi-view display module has a frameless screen so that a number of modules are tiled to provide a large screen. The module consists of a number of MEMS projectors and a lenticular lens screen, and the projected images are superimposed on the lenticular lens screen. Each module should produce a large number of viewpoints to allow many viewers in a large viewing area simultaneously.
MEMS projectors used to construct the multi-view display module consist of a biaxial MEMS scanning mirror and RGB lasers . A lens near the laser collimates the light from the laser. The light from the three lasers is then combined with dichroic elements into a single white beam. By using a beam splitter or fold-mirror optics, the beam is relayed onto the biaxial MEMS scanning mirror, which scans the beam in a raster pattern. The projected image is created by synchronously modulating the three lasers with the position of the scanned beam. In a raster-scanned laser projector, there is no projection lens. The projected beam directly leaves the MEMS scanner and creates an image on the projection screen. Because lasers are used as light sources, color matching among the projectors is not needed. The method used to generate dots constituting projected images can be flexibly altered. The MEMS projectors have low energy consumption, are compact as well as inexpensive. Because a large number of projectors must be used to obtain a large screen, the absence of the need for a projection lens reduces the total system cost. In addition, the image distortion of MEMS projectors is more easily corrected when compared to that of conventional projectors employing projection lenses. Reference 14 shows the tiling-type autostereoscopic display using MEMS projectors.
In the multi-view display module proposed in this study, images generated by multiple projectors are superimposed on a one-dimensional lens array. Yamasaki et al. proposed the combination of a projector array and two-dimensional (2D) lens array to construct an integral imaging display [16, 17] having full parallax, although the system proposed in this study is based on the multi-view display technique having horizontal parallax. They demonstrated the integral imaging display using 15 projectors. Said et al. showed the visual quality analysis of autostereoscopic displays, and theoretically showed that the combination of a projector array and lens array will improve the visual quality .
The proposed technique provides only horizontal parallax, although the earlier technique [16–18] provides both horizontal and vertical parallax. However, the proposed technique is designed to yield more viewpoints in the horizontal direction and a higher resolution compared with the earlier technique. This can be achieved by controlling the dot-generation scheme of the MEMS projectors. The MEMS projectors have the capability of flexibly controlling the dot positions. Therefore, the proposed technique is not only a straightforward simplification of the earlier technique, but it also effectively utilizes the advantage of MEMS projectors. Moreover, double lens surfaces are used as the screen to form a viewing area in front of the screen, although the earlier technique used a single lens surface.
The configuration and operating principle of the proposed display module are presented in Sec. 2, the experimental display system is explained in Sec. 3, and the experimental results are shown in Sec. 4. The discussion is given in Sec. 5, and our conclusions are given in Sec. 6.
2. Multi-view display module
The proposed multi-view display module is depicted in Fig. 3 . The module consists of an array of MEMS projectors, a vertical diffuser, and a lenticular lens. All MEMS projectors have different horizontal positions. All images generated by the MEMS projectors are superimposed on the vertical diffuser. The lenticular lens having double lenticular surfaces is located in front of the vertical diffuser.
Figure 4 shows the horizontal sectional view of the multi-view module. Figures 4(a)–4(c) show the paths of rays emitted from three projectors located at different horizontal positions. Rays from projectors are converged by cylindrical lenses on the rear lenticular surface to generate light spots on the front lenticular surface, and then deflected by the cylindrical lenses on the front lenticular surface. By placing the focal plane of the front lenses on the rear lenticular surface, all light spots emit rays in the same manner, as shown in Fig. 4. These light spots work as 3D pixels because multiple dots on an identical horizontal scan line generated by the MEMS projector, which correspond to one cylindrical lens, generate different viewpoints of the multi-view module, i.e., rays from the multiple dots are reflected to different horizontal directions. The horizontal position of the 3D pixel is determined by the horizontal position of the projector. Because all projectors have different horizontal positions, the 3D pixels are produced at different horizontal positions in each cylindrical lens. The number of 3D pixels in each cylindrical lens is equal to that of the projectors.
Figure 5 shows the vertical sectional view of the multi-view module. Because rays are diffused vertically by the vertical diffuser, the difference between the vertical positions of the projectors is practically eliminated. Therefore, as shown in Fig. 6 , the 3D pixels generated by different projectors are aligned in the horizontal direction, even though the projectors have different vertical positions. Thus, the total number of 3D pixels of the multi-view module in the horizontal direction, i.e., the horizontal resolution of the multi-view module, is the number of cylindrical lenses constituting the cylindrical lens magnified by the number of projectors. The horizontal resolution can be increased by increasing the number of projectors.
To generate a 2D array of dots, the MEMS projectors modulate the optical power of the laser during scanning the laser beam two-dimensionally. By properly modulating the laser, the horizontal positions of the dots can be changed among horizontal scan lines corresponding to one 3D pixel, as shown in Fig. 7 . Rays from dots at different horizontal positions are refracted by the cylindrical lens to generate different viewpoints of the multi-view module. The number of viewpoints can be increased by increasing the number of horizontal scan lines corresponding to one 3D pixel, which is denoted by S and shown in Fig. 7.
Because the screen of the module can be made larger than the cross section required for the projector array, a frameless screen can be realized. Therefore, a 2D array of the multi-view modules can be aligned seamlessly so that the screen size can be increased.
The specifications of the multi-view display module are described. The number of projectors is denoted by N, and the resolution of the MEMS projectors is denoted by X × Y. The number of cylindrical lenses constituting the lenticular lens is denoted by L. Then, the 3D resolution of the module is given by (NL) × (Y/S), and the number of viewpoints is given by XS/L.
Now, the calculations for the optical system design are described. The length between the projectors and diffuser is denoted by l. The focal length and lens pitch of the rear lenticular surface are denoted by f and p, respectively. Assuming that l is much larger than f, the front lenticular surface where the 3D pixels are generated is approximately located at a distance of f from the rear lenticular surface. Then, the focal length of the front lenticular surface should also be f in order to give an identical ray divergence to all 3D pixels. Because the 3D pixels are generated at slightly outer positions relative to the rear cylindrical lens, the lens pitch of the front lenticular surface should be (1 + f/l)p, which is slightly larger than that of the rear lenticular surface. The horizontal pitch of the 3D pixels is given by (1 + f/l)p/N, and the horizontal pitch of the MEMS projectors is given by (1 + l/f)p/N. The viewing zone angle of the module, which is denoted by ϕ shown in Fig. 4, is given by ϕ = 2 tan−1(p/2f).
The positions where 3D pixels are generated in the proposed system is not affected by the image distortion of the MEMS projectors. The alignment of the MEMS projectors significantly affects the positions of the 3D pixels because the horizontal positions of the MEMS projectors determine the horizontal positions of the 3D pixels. Therefore, the 3D pixels can be generated stably compared to the former two types described in Sec. 1. The image distortion of the MEMS projectors affects the directions of rays emitted from the 3D pixels, i.e., the generation of viewpoints. The image distortion of the MEMS projector is less complicated when compared to the conventional projectors employing projection lenses because the distortion caused by the mechanical scan can be more easily analyzed than that caused by aberrations of the projection lenses.
3. Experimental system
In order to verify the suitability of the proposed technique to construct the multi-view display module, an experimental display system was constructed.
Four MEMS projectors were used to construct the MEMS projector array. The MEMS projectors were SHOWXX + TM, which are commercial products provided by MicroVision Inc. The resolution was 848 × 480, which was the number of dots generated by the projectors. The frame rate was 60 Hz. The wavelengths of the R, G, and B laser lights were 642 nm, 532 nm, and 442 nm, respectively. The projectors were connected to PCs via the connection docks. Because the scan angle of the projectors was limited, four images generated by the four projectors were partially superimposed, as shown in Fig. 8 . Because the scan area was positioned above the projectors, two projectors were located at the upper position and the other two projectors were located at the lower position. The two upper projectors were fixed in an upside down position. The scanning plane was located at the distance of 440 mm from the projector array, and the size of the common screen area was 302 × 206 mm2 (14.4 in). The number of dots in this common screen area was 640 × 480. Because the two outer projectors could not fully cover the common screen area, the left and right areas with a width of 59 mm were covered with three projectors.
For the vertical diffuser, a lenticular lens with a fine lens pitch was used. The lenticular lens was placed so as to align the cylindrical lenses in the vertical direction, allowing the vertical diffusion of rays.
Two identical lenticular lenses were combined to obtain the double lenticular surfaces. The lens pitch of the front lenticular lens should be slightly larger than that of the rear lenticular lens, as described in Sec. 2. Because it was difficult to obtain two lenticular lenses with slightly different lens pitches, two identical lenticular lenses were used. The dimensions of the lenticular lens were identical to those of the common screen for the MEMS projector array. The number of lenses was 40, and the lens pitch was 7.55 mm. The focal length was 11.4 mm. Therefore, the two lenticular lenses were separated by a length of 11.4 mm.
Four scan lines of the MEMS projectors corresponded to one 3D pixel. The number of dots in one scan line corresponding to one cylindrical lens constituting the double lenticular lens was 16. Therefore, the 3D resolution, i.e., the number of 3D pixels, of the experimental display system was 160 × 120, neglecting the decrease in the number of 3D pixels in the left and right areas of the screen due to the incomplete image superposition described above. The number of viewpoints was 64, and the viewing zone angle was 36.6°.
Because the MEMS projectors used to construct the experimental system were commercial products, laser modulation scheme was fixed and could not be changed, i.e., dots were generated on a non-slanted 2D grid. Therefore, instead of changing the laser modulation scheme, a slanted slit array was placed on the scanning plane to obtain the slanted dot arrangement, as shown in Fig. 7. The slit array needs to be designed to transmit different horizontal portions of dots located in the same column corresponding to one 3D pixel. Thus, the slits were slanted at an angle of tan−1(1/S). The pitch of the slits was equal to the horizontal pitch of the 3D pixels, i.e., p/N. The width of the slits is equal to the pitch of the slits divided by the number of scan lines corresponding to one 3D pixel, i.e., p/NS. Because the experimental system used four scan lines to construct one 3D pixel, the slant angle was 15.4°, pitch was 0.472 mm, and width was 0.188 mm. The slit array was fabricated by forming an emulsion mask on a glass plate. Figure 9 shows the fabricated slit array.
The image distortion of the MEMS projectors was measured in advance, and the distortion was corrected by anti-distorting the displayed image electronically. The MEMS projectors had pincushion distortion and the average image distortion was 2.68%, which was subsequently improved to 0.85% by the image correction.
A photograph of the constructed display system is shown in Fig. 10 . The display screen consisted of the slit array, the vertical diffuser, and two lenticular lenses, and they were fixed in the aluminum frame. Because the aim of this study is to verify the proposed display technique, we did not construct a frameless screen.
4. Experimental results
We confirmed that there was an increase in the number of 3D pixels in the cylindrical lenses due to an increase in the number of projectors. The number of projectors that project images was changed from one to four. All projectors projected white images. The magnified images of the center part of the display screen in Fig. 11 show the generation of the 3D pixels. The number of 3D pixels in the cylindrical lenses increased with the number of projectors.
The 3D image generated by the experimental display system is shown in Fig. 12 . The photographs were captured from different horizontal directions. Proper parallax was obtained, and the 3D image had smooth motion parallax.
From Fig. 12, vertical black lines were observed in the 3D images, which appeared more frequently in the left and right areas than in the center. Vertical bright lines were also observed in the 3D images. The flicker was not observed. Because laser lights were used, speckles were observable. However, the speckles in 3D images were not so apparent as compared to those in 2D images generated by the MEMS projector on a normal screen.
The vertical black lines appeared in the 3D image because of two reasons. First, the left and right parts of the display screen were covered by only three projected images, as described in Sec. 3, so there were three 3D pixels in the cylindrical lenses. Second, the lens pitch of the front lenticular surface should be 7.75 mm, which is slightly larger than that of the rear lenticular surface, i.e., 7.55 mm. However, we used identical lenticular lenses for both surfaces. Therefore, the rays from the 3D pixels generated by the rear cylindrical lenses were not correctly deflected by the front cylindrical lenses, and several 3D pixels could not be observed from the observed positions. These missing 3D pixels exist along the vertical direction and caused the vertical black lines to appear. They can be eliminated by increasing the scan angle of the MEMS projectors and using a double lenticular lens with different lens pitches for both surfaces. The rays from some of the missing 3D pixels, which were incorrectly deflected by the front cylindrical lenses, were observed from incorrect viewpoints. These incorrectly deflected rays led to the formation of the vertical bright lines in the 3D images. They can be eliminated using a double lenticular lens with different lens pitches for both surfaces.
From Fig. 11, the 3D pixels in the same row do not have exactly the same vertical positions; their vertical positions differed slightly. This may be because of the gap between the slit array and vertical diffuser. The images generated by the four projectors were superimposed on the slit array so that the vertical diffuser was not placed exactly on the superposition plane, as shown in Fig. 5.
From Fig. 11, we observed that the 3D pixels were not equally spaced in the horizontal direction. This was caused by the aberration of the cylindrical lenses of the lenticular lens. We confirmed the generation of the 3D pixels by using an optical design software and found that the positions of 3D pixels generated by the rear cylindrical lenses were nearer to the lens axes than the positions expected by the paraxial approximation. The distances between two adjacent 3D pixels belonging to adjacent cylindrical lenses were larger than those between adjacent 3D pixels belonging to an identical cylindrical lens. The non-uniformity in the horizontal pitch of the 3D pixels may be reduced by adjusting the horizontal positions of the MEMS projectors.
The separation of dots was observable in the generated 3D images; i.e., the 3D pixels were separately generated. The dot separation was caused by the horizontal separation of the MEMS projectors. Thus, when the number of projectors in the module increases, the gap between the dots decreases. The dot separation may not be perceptible when a large number of modules are tiled to construct a large display screen, such as a large-screen 2D display consisting of a large number of LED dot-matrix modules.
From Figs. 11 and 12, no differences in the color representation of the 3D pixels were observed. The MEMS projectors use laser diodes as the light sources so that the color matching among the projectors is not required.
In the experimental display system, the slit array reduced the light intensity by a factor of four. Moreover, the light intensity of the laser beams from the MEMS projectors was not high. However, the generated 3D images were not as dark as was thought because the experimental display system diffused light only in the vertical direction, and multiple projectors were used. The modulation of lasers to enable the direct generation of the slanted dot array will remove the slit array. In addition, the use of more projectors will improve the brightness of the 3D images.
Speckles are the result of interference among lights diffused by a random surface. In the proposed technique, the laser light is diffused in the vertical direction, and is not diffused in the horizontal direction. Moreover, there is no interference between lights from different MEMS projectors. Therefore, the generation of the speckles in the 3D images was less obvious than that of the speckles in the 2D images generated by the MEMS projectors on a normal projection screen.
The experimental display system was designed so that all 3D pixels emit light in the same manner in the horizontal direction. To maximize the width of the viewing area at a specific distance from the display screen, as the positions of the 3D pixels approach the left and right sides of the screen, the 3D pixels should emit light in a more inward direction. This can be achieved by changing the design of the double lenticular lens or by attaching a lens to the display screen. When multiple modules are used to obtain a large screen, the adjustment must be done for each module. Therefore, the latter method may be preferable.
The multi-view display module employing a MEMS projector array was proposed to realize an ultra large-screen 3D display. The proposed multi-view module is based on the technique that generates multiple 3D pixels in each cylindrical lens of a lenticular lens located on the screen. The module can provide a frameless screen so that multiple modules can be aligned seamlessly to obtain an ultra-large screen. The experimental display system was constructed using four MEMS projectors. The module had a 3D resolution of 160 × 120, and it provided 64 views. The screen size was 14.4 in. The generation of the 3D pixels was confirmed, and the 3D images were successfully generated.
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