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We propose a novel multiplexing technique for increasing the viewing zone of a multi-view based multi-projection 3D display system by employing double refraction in uniaxial crystal. When linearly polarized images from projector pass through the uniaxial crystal, two possible optical paths exist according to the polarization states of image. Therefore, the optical paths of the image could be changed, and the viewing zone is shifted in a lateral direction. The polarization modulation of the image from a single projection unit enables us to generate two viewing zones at different positions. For realizing full-color images at each viewing zone, a polarization-based temporal multiplexing technique is adopted with a conventional polarization switching device of liquid crystal (LC) display. Through experiments, a prototype of a ten-view multi-projection 3D display system presenting full-colored view images is implemented by combining five laser scanning projectors, an optically clear calcite (CaCO3) crystal, and an LC polarization rotator. For each time sequence of temporal multiplexing, the luminance distribution of the proposed system is measured and analyzed.
© 2016 Optical Society of America
1. Introduction
A basic technology of autostereoscopic three-dimensional (3D) display is multiplexing spatial information of two-dimensional (2D) display into 2D images with angular information by sacrificing some portion of spatial resolution. Special optical components such as lens array, parallax barrier, and rotational mirror act as devices for implementing the multiplexing. Since the 2D image with directivity provides the parallax with changes in observing position, it is possible to induce the depth perception cues of binocular disparity, motion parallax, convergence, and accommodation response [1–6]. However, the capacity of the original 2D image is limited in the bandwidth of display device, and the maximum capacity is inefficient to providing natural parallax with high resolution corresponding to the resolution of state-of-the-art 2D display device.
For overcoming the limitation in bandwidth of display device, multi-projection 3D display with stacking projectors in both horizontal and vertical directions was proposed. The multi-projection 3D display is a kind of spatially multiplexed autostereoscopic displays [7, 8]. By the virtue of the projection system, it is possible to concentrate the capacity of image information into defined area. Besides, since each image has inherent directivity according to the orientation of projectors, the spatial and angular resolution can be improved simultaneously. The degree of freedom in scaling of projection image is definitely greater than that of flat panel display. Based on those advantages, many researchers reported multi-projection 3D display systems [9–13]. In spite of clear 3D image quality, scalability, and fine viewing parameters, the reliability of the driving system is quite low, and power and computational errors could be accompanied. Furthermore, the cost issues and complex system structure act as an obstruction for practical uses [9, 12]. For reducing the bulky size of the system, short throw projection methods with freeform lens or multiple folding of optical path were proposed [14–16]. Meanwhile, high cost for many projectors and complex operating system remain to be solved for popularization of the system. There were techniques reducing the complexity of multiple projectors array, and their operation systems used temporal multiplexing. Jones et al. proposed the 360-degree light field 3D display with rotation mirror and a digital micromirror device (DMD) projector [6]. The rotation mirror and DMD projectors were synchronized to present correct light field toward reflection direction according to the orientation of rotating mirror. Teng et al. implemented the super multi-view system with high-density light field 3D display system by using rotational filter mask [17]. The optical path of image from organic light emitting diode (OLED) array is selectively determined by the time-variable pinhole distribution of rotational filter mask. Takaki et al. fabricated micro electro mechanical system (MEMS) projection setup, which was specialized for multi-projection 3D display system with horizontal scanning [18]. The system consists of mirror galvanometer for horizontal scanning and MEMS device for presenting gray scale of image. Mirror galvanometer sweeps the image forward angular direction and the 3D images are reconstructed by collimation optics. The system has compact size of entire system, but the cost of components such as mirror galvanometer and MEMS device is quite expensive, and it is hard to represent the full-color images with three primary colors because there are limitations in modulation speed of image via MEMS device and mirror galvanometer. Those methods reconstruct fine 3D images, but the mechanical movement of rotational optical component accompanies safety and reliability issues.
Some researchers reported electrically controllable temporal multiplexing technique without the mechanical movement. By virtue of birefringent material, polarization multiplexing of projection-based system can be realized. Akşit et al. proposed a simple method for generating stereoscopic projection system by using a single projection unit combined with a polarization rotator [19]. By altering the polarization state of image from projector in real-time, the observer wearing polarization glasses sequentially perceives correct view images as the case of stereoscopic television. Recently, Liu et al. proposed a novel super multi-view three-dimensional display technique by applying the dynamic gating aperture [20]. The position of the aperture is switched in temporal sequence and the multiple viewpoints are effectively generated through each aperture. The system provides good 3D image quality and has small form factor for portable device, but it is hard to illuminate large screen due to the limitation in brightness of OLED and multiple sequences.
Park et al. proposed the novel concept of polarization multiplexing technique using uniaxial crystal [21]. According to the polarization states of light, the optical path can be modulated when the light passes through the uniaxial crystal. By altering the polarization state of elemental image of integral imaging in sequence, two different central depth planes are formed along longitudinal direction, and the depth expression range of integral imaging system is extended. Likewise, the polarization multiplexing technique for liquid crystal on silicon (LCoS) using uniaxial crystal was proposed. The images from the LCoS could be formed at different positions after passing through the uniaxial crystal. The simulation results verify the feasibility of the propose system, but no practical experiments have been performed [22]. In our conference paper, concept of dual projection, which means generation of two viewing zones by a single projection unit, was proposed by adopting the uniaxial crystal [23]. The optical paths of the images from laser scanning projector split into two different directions after passing through the uniaxial crystal. Two separated viewing zones are generated at optimum viewing distance. However, the system just provides view images with single color channel like anaglyph [24], and it is hard to induce correct binocular disparity.
In this paper, viewing zone duplicated multi-projection 3D display system is implemented by adopting the principle of double refraction in the uniaxial crystal. The optical path of image from the projector can be laterally shifted in the uniaxial crystal according to the polarization state of light. Since the shifted optical path is considered as the image originated from the projector located in shifted position, the viewing zone can be formed at different viewpoints. Therefore, it is possible to generate two viewing zones separated in lateral direction using a single projection unit. Conventional projection unit has single polarization state for each primary color light source, and it is hard to generate two viewing zones with full-color. For generating the intact view images at both viewing zones generated by single projector, the temporal multiplexing technique with polarization switching is adopted for full-color generation. Since the electrical polarization switching device and the uniaxial crystal are implemented in the proposed system, no mechanical movement and bulky components are required. Through experiments, the feasibility of the proposed method is verified, and a prototype of ten-view multi-projection 3D display with five projectors is implemented. The fine viewing zone duplication is observed, and the full-color view images by temporal multiplexing with polarization switching are realized. Furthermore, the luminance distribution of the system is measured for verifying the viewing zone formation.
2. Principle
2.1 Double refraction in uniaxial crystal
Figure 1 shows double refraction in calcite crystal (CaCO3). The calcite crystal is one of the most popular uniaxial crystals widely used in the optical components such as beam splitter, prism, and beam displacer because of its unique properties of birefringence and transparency. The calcite crystal is a negative uniaxial crystal: the refractive index of ordinary wave no ( = 1.658) is greater than that of extraordinary wave ne ( = 1.486). The calculation of propagation of wave in uniaxial crystal is based on the boundary condition that all the tangential components of wave vectors along the boundary are same [25]. Since the two shells of the normal surface exist in calcite crystal, there are two possible propagation vectors according to the polarization state of the incident wave. The boundary condition between air and uniaxial crystal gives following relation:
where ki is the magnitude of propagation vector of the incident plane wave with incident angle of θi, and ko and ke are the magnitude of propagation vectors of ordinary and extraordinary waves after refraction, respectively. Those waves are refracted at the boundary with the refraction angle of θo and θe. In the case of the ordinary wave whose shape of the normal surface shell is sphere, the wave obeys Snell’s law, and the refracted angle and Pcircle, which is intersection point of the propagation vector and the normal surface shell, are obtained. From the boundary condition in Eq. (1), Pellipse where the propagation vector of extraordinary wave and the normal surface shell of the wave with the shape of ellipse intersect is also calculated by geometrical operation of ellipsoid as follows: where ω is angular frequency of the wave and c is the speed of light. Furthermore, the direction of energy flow which corresponds to the ray direction of the extraordinary wave can be obtained. Since the energy flow of the wave is perpendicular to the normal surface, the normal to gradient at Pellipse is equal to the ray direction of θe_ray:In case of the ordinary wave, the propagation vector and the direction of energy flow coincide due to the sphere-shaped shell of the normal surface. Therefore, there exists difference in ray paths between both waves [26–28]. When the plane-parallel uniaxial crystal with optic axis placed along the interface is inclined with the angle of θinclined to x-axis and the thickness of the crystal is defined as t, lateral displacement in lateral direction D between ordinary wave and extraordinary wave is equal to:
The trajectory of optical path and the displacement can be modulated by orientation of optic axis as well as incident angle of light. On the other hand, the optical path can be modulated according to purposes.
2.2 Viewing zone duplication in multi-projection 3D display
The principle of double refraction can be easily applied to multi-projection 3D display system, since many projection systems emit the polarized light (e.g. LCD type, LCoS type and laser scanning type). Provided that a laser scanning projector has three primary color sources which are s-polarized (red and blue) and p-polarized (green) respectively, the optical path of lights incident on the uniaxial crystal can be divided into two different trajectories as shown in Fig. 2(a). S-polarized red and blue lights pass through the trajectory of ordinary wave, and p-polarized green light traces the path of extraordinary wave. As a result of double refraction, those lights are parallel and propagate into the same direction with lateral displacement of D. This deviation of optical path can be considered as two spatially separated projectors one illuminates magenta color and the other illuminates green color. It will be called “dual projection” in this paper. Furthermore, the image of each viewing zone generated by dual projection can be independently modulated by changing the primary color information of input image. Since two separated projectors can contribute to forming two independent viewpoints at optimum viewing distance, the dual projection system can be adopted in multi-view based multi-projection 3D display system as shown in Fig. 2(b). Two view images originated from separated position would be converged into each viewpoint. It is expected that the series of dual projection system would double the number of viewing zones.
Fig. 2 Concept of viewing zone duplication: (a) dual projection, (b) viewing zone duplication for multi-projection 3D displays.
For analyzing the configuration of dual projection system, ray tracing is performed for both polarization states. Figure 3(a) shows the relationship between the lateral displacement and the incident angle calculated by the Eq. (5) when the optic axis is parallel to the interface, and the thickness of calcite crystal is 30 mm. The maximum lateral displacement is about 1.1 mm near the incident angle of 48°. The lateral displacement could be modulated by tilting the calcite crystal.
Fig. 3 Lateral displacement in dual projection: (a) lateral displacement with changes in incident angle, (b) projection origin shift in dual projection.
For illuminating the position of virtual projectors generated by dual projection, the path changes of diverging rays from real projector are traced in both the air and the calcite crystal. Then the origins of virtual projectors are retraced in opposite direction of propagation based on the exit position and the propagation angle at the interface. The simulation condition of incident angle is 40° for setting the lateral displacement as 1 mm. In Fig. 3(b), white solid lines present the diverging rays from the projection origin of real projector located at 42.5 mm and 26.8 mm in lateral and longitudinal direction, when the edge of uniaxial crystal is set to zero point. Magenta and green dashed lines present retraced bundle of rays of s- and p-polarized lights, respectively. The retraced rays of s- and p-polarized lights converge onto the narrow spot having the width about 240 um which is shifted from real projector position. The spots could be assumed to both s- and p-polarized projection origins. The converging area of s-polarized rays is located at 32.7 mm in lateral direction and that of p-polarized rays is located at 31.7 mm. The lateral shifts of s- and p-polarized projection origins from the real projector are 9.8 and 10.8 mm, respectively. The location of both origins in longitudinal direction is near 9 mm, but the projection origin of s-polarized light is a little behind that of p-polarized light. This configuration can affect the longitudinal position or luminance distribution of viewpoints. Since the projection origin shift leads to the image shift at the screen, the image shift is also calculated by the geometrical relationship between the origins. As estimated in the Fig. 3(a), it is confirmed that the lateral displacement calculation is valid for diverging rays and virtual projectors generated by dual projection are well separated in lateral direction.
Based on the lateral displacement simulation, the parameters of optimum viewing position and viewpoint interval are calculated in multi-projection 3D display. The optimum viewing position of dv is calculated by lens maker’s law and the interval of viewpoints pdual is determined by distance relationship between lens and projection origin:
where dp is the distance between projection origin and Fresnel lens, and f is the focal length of Fresnel lens. The interval of viewpoints generated by dual projection is calculated by the magnification of the system.Consequently, it is possible to increase the viewing zones effectively, and the density of viewing zone can be increased or the system load can be reduced to the half of the conventional system.
2.3 Full-color generation of dual projection
As shown in the Fig. 2(b), the p-polarized viewing zones are lack of green color and the s-polarized viewing zones present only green color. This configuration is similar to the anaglyph – one of the early stereoscopic 3D display technologies, which provides binocular disparity by means of the color filtering glasses. Since lack of color information for monocular eye cannot induce perfect 3D image perception, there was an attempt to switch colors in the anaglyph by using temporal multiplexing [23]. Likewise, it is possible to generate full-color 3D images in the proposed method by virtue of polarization modulation.
The basic principle of the full-color representation in the display device is controlling the gray level of three primary colors: red, green, and blue. Therefore, sequential path switching of colors enables the system to generate the full-color in the proposed method. Figure 4 shows the schematic diagram of polarization-based temporal multiplexing for full-color generation. In case of the system, the color of viewpoints will be switched by altering the polarization states of magenta and green images with 90° rotations of its vibration axis. The LCD acts as a polarization rotation, and it is easy to implement the polarization switching by changing the voltage of the LCD device. In the first sequence for the Nth real projector without any polarization modulation, the s-polarized magenta image and the p-polarized green image are presented onto the (2N-1)th and 2Nth viewpoints, respectively. Then, the LCD rotates the polarization of both images by 90°, and the optical paths of images are switched in the second sequence. When the switching speed of the polarization is as fast as the critical flicker fusion frequency so that human cannot perceive the changes in both sequences, the magenta and green images are adequately synthesized, and the observer will perceive the full-color view images at each viewing zone.
2.4 Image processing for full-color generation
Figure 5 shows the interweaving process of two adjacent view images for full-color generation. Since input image for real projector contributes to representing two adjacent view images, the input image should include both adjacent view images. Assuming the magenta view image is formed at (2N-1)th viewpoint, and the green view image is formed at 2Nth viewpoint in the first sequence, the input image should be modulated for representing the correct view information simultaneously. Therefore, the magenta (2N-1)th view image and the green 2Nth view image are interweaved as the first sequence input image for Nth real projector. Synthesized view image will be divided into both (2N-1)th and 2Nth view images, respectively. Thus, the second sequence is generated by interweaving the magenta 2Nth view information with the green (2N-1)th view information. Consequentially, the s-polarized (2N-1)th view image and the p-polarized 2Nth view image will be observed at corresponding viewpoints with full-color. With the changes in sequence, the input voltage of LCD device should be synchronized for rotating the polarization states of input images.
3. Experiments and results
3.1 Prototype of ten-view multi-projection 3D display with viewing zone duplication
Prototype of ten-view multi-projection 3D display system applying dual projection is implemented for illuminating the feasibility of the proposed system. Moreover, luminance distribution measurement of the proposed system is performed with the changes in polarization states in each sequence.
Figure 6(a) shows the experimental setup of ten-view multi-projection 3D display system with five laser scanning projectors, LCD of polarization rotator, the calcite crystal as uniaxial crystal, and collimation optics. The laser scanning projectors (MicroVision, SHOWWX+) are stacked in vertical direction, and the horizontal position of each projector is set to maintain the uniform gap between adjacent projectors. The projector array and polarization switcher of polarizer-detached LCD (ODHitec, OD121S1LG-TAS) is synchronized for full-color generation. For aligning polarization axis of the laser scanning projector and polarization rotator, the polarization states of laser diode sources in the laser scanning projector are measured by the polarimeter (Thorlabs, PAX7510IR1-T), and the detailed polarization information of each source is shown in Table 1. The calcite crystal is inclined with the angle of 40° for duplicating projectors with uniform separation. The inclined angle of the calcite cube is calculated by the Eq. (5) for the condition that the lateral displacement is 1 mm. The yellow points indicated in the Fig. 6(c) correspond to projection origins of the proposed system, and it is confirmed that the ten virtual projectors are generated by five real projectors with the calcite crystal. Neutral density filter having transmittance of 0.391% is inserted in front of projector array for protecting eyes and sensors. The anisotropic diffuser expands the viewing region in vertical direction, and the Fresnel lens of 150 mm focal length is located at 170 mm from the projection origin to form the viewing zone at optimum viewing distance. The detailed experimental conditions are shown in Table 2.
Fig. 6 Experimental setup: (a) prototype of proposed system, (b) luminance measurement of prototype, and (c) duplicated projection origins.
Table 1. Detailed polarization information of laser diode sources.
Table 2. Experimental conditions
Figure 7 shows the color conversion of the proposed system. When the polarization states are switched by changing the gray level of the LCD polarization rotator, the color of view images is also switched simultaneously. The color balance of each viewpoint is not uniform because the azimuthal angles of polarization of red and blue sources are slightly different, and the polarization axes of magenta (red and blue) and green sources are not perfectly orthogonal as indicated in the Table 1. In addition, some amount of unintended color information from the ellipticity of red and blue sources acts as noises at each viewpoint. Though the color uniformity of both sequences is low, the color conversion in multiplexing process is verified. The uniformity can be improved by modulating the polarization state of each source to have well-defined linear polarization and geometry of the sources to have parallel or orthogonal relationship. When the fast switching of input sources for projector and polarization rotator is realized, the magenta and green images are synthesized, and the observer perceives the full-color view images. Visualization of polarization switching and temporal multiplexing for full-color generation is provided in the Fig. 7. The cycle of temporal multiplexing is 1/15s, and the visualization is recorded by 24 frames per second. Black offset images are inserted between adjacent sequences because the response time of the LC polarization rotator is slower than the image switching speed of the laser scanning projector. The noises originated from the slow rising and falling time of LC response can be minimized by adopting the fast polarization switching devices such as ferroelectric LC.
By combining the five laser projectors and the polarization rotator, the viewing zone duplicated ten-view multi-projection 3D display is realized. Figure 8 shows the series of captured view images generated by the prototype. The prototype is operated with 15 frames per second, and the view images are captured at optimum viewing distance of 1275 mm during 1/8 s of shutter speed. The interval of capturing corresponds to the interval of viewpoints of 7 mm. The view images are clearly separated with the parallax. A movie containing parallax of the system is provided in the Fig. 8. As mentioned earlier, though the odd-numbered (s-polarized) images are reddish and the even-numbered (p-polarized) are greenish because of the noise from the inherent source property, the sequential images are synthesized, and the full-color images are observed at every viewpoint in real-time. The quality of the images is affected by the low resolution of projectors, laser speckle from laser diode sources, and diffraction from the pixelated structure of polarization rotator of LCD. We expect that the high resolution projector with speckle reduction and diffraction-free polarization rotator can improve the image quality. The results verify the feasibility of the dual projection and the full-color generation by polarization switching.
Fig. 8 Series of full-color view images generated by ten-view multi-projection 3D display system (Visualization 2).
3.2 Luminance distribution of the proposed system
For analyzing the viewing parameters such as the viewpoint interval and the noise, the luminance distribution of viewpoints is measured in horizontal direction [29, 30]. Figure 6(b) shows the luminance measurement setup of the prototype. The display color analyzer (Konica Minolta, CA-210) with 1 mm aperture is implemented for measuring the luminance distribution at the calculated optimum viewing position. The range of the measurement is from 50 mm to 180 mm with the sampling interval of 1 mm in horizontal direction. Since the full-color viewpoint is generated by switching of colors in the proposed method, two-step measurement is adopted for each sequence and the luminance values of each step are added for obtaining the luminance distribution at each viewpoint as follows:
where Ln_1st and Ln_2nd are the luminance values of the first and the second sequence of nth viewpoint, respectively. The Ln is the peak luminance value of nth viewpoint. When the total number of viewpoints and the measured total luminance at nth viewpoint are defined as P and Ln_total, the noise to total luminance ratio Cn at the nth viewpoint is calculated by comparing the peak luminance value of corresponding viewing zone and the summation of luminance values from unintended viewing zone as follows:The measured luminance distribution of ten viewpoints in prototype is plotted as shown in Fig. 9. The set of peaks shows the luminance distribution of ten viewpoints at the optimum viewing distance. The normalized luminance distribution as shown in the Fig. 9(b) clearly shows that the viewing zone is well duplicated by the dual projection system, and the viewpoints are separated with the uniform gap of 7 mm. The feasibility of the proposed system is verified again through the luminance distribution.
Fig. 9 Luminance distribution of prototype: (a) luminance distribution and crosstalk, (b) normalized luminance distribution.
Meanwhile, the luminance value of even-numbered viewpoints (p-polarized) is greater than that of odd-numbered viewpoints (s-polarized). In the previous section, the uniformity issue arises from polarization state of sources. Another factor affecting the uniformity is revealed in the luminance measurement. The difference in projection origin of virtual projectors also raises the uniformity issues. In the Fig. 3(b), the projection origin of virtual projectors is separated in longitudinal direction as well as lateral direction according to the polarization state of light. Though the longitudinal displacement is less than the lateral displacement, the position of viewpoint generated by virtual projectors would be slightly different in longitudinal direction. Therefore, the captured number of converged rays onto each viewpoint can be altered when the probe of display color analyzer is fixed in longitudinal direction. The result shows that the viewpoint formed by p-polarized light is close to the probe, and the viewpoint formed by s-polarized is far from the probe. The uniformity issue could be also found in the normalized luminance distribution by comparing the sharpness of peaks. The peak of the p-polarized viewpoints is sharper than that of the s-polarized viewpoints. In other words, the compositive factors of polarization states and projection origin lead to the uniformity issues and high noise ratio of 53% on average. The uniformity can be mitigated by weighting the input images and optimizing the system design for minimizing the longitudinal shift.
4. Conclusion
Viewing zone duplication of multi-projection 3D display is realized by using double refraction in uniaxial crystal. In the uniaxial crystal, two possible optical paths exist, and the path can be determined according to the polarization state of light. Dual projection system contributes to forming two different viewing zones at the optimum viewing distance. Therefore, the number of viewing zones in the multi-view system is doubled compared to the conventional system. Furthermore, the full-color image is generated by adopting the temporal multiplexing technique with the real-time polarization switching. The experimental results show that the prototype forms full-color ten viewpoints with five projectors. The luminance distribution at viewing area is measured for analyzing the viewing parameter of view interval and noise. It is confirmed that the adjacent viewpoints generated by dual projection are well separated with the interval of 7 mm. The average value of crosstalk is about 53%. Possibilities of improvement in image quality and reduction in noise are discussed: fast-response and diffraction-free polarization switching device, high-resolution projection unit, and accurate alignment of polarization axis. We expect that the proposed method can be applied in the display system emitting the polarized light such as LC-based display system, laser source based display system, and OLED having circular polarizer. The capturing system obtaining the 3D information such as light field camera and light field microscopy can be applications of the proposed system. In particular, the concept of the proposed method would be directly implemented in the light field based multi-projection 3D display system with extended exit pupil beyond the limitation in densely stacking projectors originated by physical dimension of the device [31].
Acknowledgment
This research was supported by “The Cross-Ministry Giga KOREA Project” of The Ministry of Science, ICT and Future Planning, Korea [GK15D0200, Development of Super Multi-View (SMV) Display Providing Real-Time Interaction]. The car 3D image used in the experiment is provided by aXel used under Creative Commons Attribution 3.0.
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