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A technique to enhance the depth range of the multi-layer light field three-dimensional display is proposed. A set of the optical plates are stacked in front of the conventional multi-layer light field display, creating additional internal reflection for one polarization state. By switching between two orthogonal polarization states in synchronization with the displayed three-dimensional images, the depth range of the display can be doubled. The proposed method is verified experimentally, confirming its feasibility.
© 2013 Optical Society of America
1. Introduction
Autostereoscopic three-dimensional (3D) displays present depth sensation to observers without requiring special viewing aids like stereoscopic glasses [1]. Most autostereoscopic 3D display techniques use an optical plate like a parallax barrier or a lens array that guides the light rays from an image panel to the specific directions [2–4]. This optical plate transforms the two-dimensional (2D) spatial distribution of the pixels in the display panel to four-dimensional (4D) spatio-angular light ray distribution, or also called light field, that corresponds to the desired 3D scene [5–7]. Increased dimensionality along with the fixed structure of the optical plate brings inherent reduction of the spatial resolution of the displayed 3D images by a fixed ratio, regardless of its depth distribution.
Recently, a multi-layer light field display, or called a tensor display has been proposed and attracts considerable attentions [7–10]. Instead of the fixed optical plate and the image panel, the multi-layer light field display uses a stack of the multiple transmission-type panels. As shown in Fig. 1, the light rays are modulated spatially and angularly as they pass through the panel stack, reconstructing the light field of the desired 3D scene. Since the light field is reconstructed by the dynamic devices, the multi-layer light field display can control adaptively the spatial resolution reduction ratio according to the desired 3D scene. This unique feature brings significant resolution enhancement especially when the depth of the 3D scene is small. As the depth of the 3D scene increases, however, the resolution enhancement over conventional autostereoscopic displays quickly disappears, limiting available depth range.
In this paper, we propose a method to enhance the depth range of the multi-layer light field display. On top of the conventional multi-layer light field display, we add a few optical layers for polarization dependent internal reflection. The added layers increase the apparent distance of the displayed images of one polarization, while leaving it unchanged for another orthogonal polarization. Hence by time-multiplexing two polarizations in synchronization with the displayed images, the depth range can be doubled, maintaining high resolution. In the following sections, we explain the depth range of the multi-layer light field display and how it can be enhanced by the proposed method. We also present experimental results for verification.
2. Depth range limitation of a multi-layer light field display
The depth range of the multi-layer light field display is determined by the depth dependent spatial resolution of the 3D images. The spatial resolution of the 3D images in a multi-layer light field display was analyzed by G. Wetzstein et al. [7]. In this section, the depth range limitation is briefly explained following the G. Wetzstein et al.’s analysis.
The spatial resolution of the 3D images is given by the maximum spatial frequency of the light field supported by the display without aliasing. The spatio-angular spectrum of the light field at a reference plane (z = 0) Ln which is generated by a n-th single display panel located at z = zn is given by
where (fx, fθ) are the spatio-angular frequency pair, Gn is the spatial frequency spectrum of the image on the n-th panel. Given the pixel pitch p of the display panel, the bandwidth of the panel is 1/2p, as shown in Fig. 2(a). The spatio-angular spectrum of the light field generated by a stack of the multiple panels is given by the 2D convolution of the individual light field spectrum Ln of each display panel. Assuming that all display panels have the same pixel pitch and are uniformly spaced by a gap g around a reference plane z = 0, the final spectrum of the light field is given by rhombus or hexagon shape for two-panel or three-panel cases, respectively. The rhombus solid line in Fig. 2(b) shows the spectral area of the two-panel case. The light field spectrum of the conventional autostereoscopic displays can also be obtained by the similar analysis [11]. The rectangular dotted line in Fig. 2(b) shows the spectrum of an integral imaging display with a panel pixel pitch p and the number of the angular light rays Nθ at each spatial position in the panel.
Fig. 2 Depth dependent resolution characteristic of a multi-layer light field display (a) Light field spectrum of a single panel, (b) Resolution of a depth slice in a multi-layer display and conventional displays.
The area defined by the solid and dotted lines in Fig. 2(b) indicates the spectral area that can be supported by the display systems. In this area, the light field spectrum that corresponds to a depth slice at z = z of the 3D image is given by a line fθ = zfx [5]. Therefore, the maximum spatial frequency fx,max that can be supported by the display system for the depth slice at z = z is given by the intersection between the spectral area and the slanted line as shown in Fig. 2(b) [7].
From Fig. 2(b), it is clear that the multi-layer light field display exhibits significantly higher resolution than conventional autostereoscopic display when the depth of the image is small. For larger depth images, however, the resolution of the multi-layer display converges to that of the conventional displays. Therefore, if the available depth range of the 3D display is determined by the tolerable minimum resolution, the depth range of the multi-layer light field display is only comparable to that of the conventional displays without any enhancement.
3. Proposed method to enhance the depth range
In the proposed method, the depth range of the multi-layer light field display is doubled by a polarization dependent internal reflection structure. Figure 3 shows the configuration of the proposed method. On top of the multi-layer display, a polarization control panel (PCP), two quarter wave plates (QWPs), a half mirror (HM), and a reflective polarizer (RP) are stacked. With respect to global coordinates x and y, the optical axes are aligned such that the PCP makes x or y linear polarization, the fast axes of two QWPs are slanted by ± 45° to x-axis respectively, and the RP reflects y linear polarization while transmitting x linear polarization.
The x linear polarized light from the PCP is transformed to a circular polarized light by the first QWP, passes through the HM, and is then transformed back to the original x linear polarized light by the second QWP. The x axis is the transmission axis of the RP, and thus the light passes through the RP and reaches the observer without any additional reflection. On the contrary, the y linear polarized light from the PCP is reflected back by the RP after its first trip through the first QWP, the HM, and the second QWP. The reflected y linear polarized light is then transformed to a circular polarized light by the second QWP, is reflected back toward the observer by the HM, and is transformed to linear polarization again by the second QWP. Since the light passes the same second QWP twice this time, the linear polarization direction of the light is now transformed to the x direction which is the transmission axis of the RP, reaching the observer. Due to the additional reflections by the RP and the HM, the apparent distance of the image from the observer increases by two times of the gap between the RP and the HM this case [12,13]. By adjusting this apparent distance to the inherent depth range of the multi-layer display, the effective depth range of the system can be doubled with time-multiplexing operation of two polarization modes.
4. Experiment
In our experiment, a multi-layer light field display was implemented using three liquid crystal (LC) panels. The parameters of the implemented multi-layer light field display are listed in Table 1. Three LC panels of the multi-domain in-plane-switching (IPS) LC mode were stacked with 5 mm spacing using two transparent acrylic plates of 5 mm thickness. The original polarizers of the LC panels were removed except the front face polarizer of the top panel and the rear face polarizer of the bottom panel, i.e. polarizers on the first and the last surfaces of the panel stack. A custom-made backlight unit of 20,000 cd/m2 luminance was attached after the bottom panel to compensate the brightness loss of the panel stack.
Table 1. Parameters of the implemented multi-layer light field display
On top of the implemented multi-layer light field display, the polarization dependent internal reflection configuration was added. A stack of a PCP, two QWPs, a HM, and a RP was attached in front of the multi-layer light field display as illustrated in Fig. 4. As the PCP, another LC panel which is the same as that used in the panel stack was used. The gap d between the HM and the RP was 20 mm, creating 40 mm increase of the apparent distance for one polarization. Since the size of the RP was only 25 mm × 25 mm in our implementation, the maximum size of the 3D image that undergoes double internal reflection was limited by that size. Figure 5 shows the picture of the implemented system.
The transmittance characteristics of the panel stack in the multi-layer light field display was characterized experimentally. Figure 6(a) shows the measured transmittance curve of a stack of two panels. The measurement result shown in Fig. 6(a) agrees well with the Date et al.’s theory [14] and indicates that the transmittance can be approximated to the linear addition of the transmittances of the individual panels in the low gray level range. Figure 6(b) shows the transmittance of the three-panel case. In our experiment, we confined the gray level range of each panel to the area indicated by the red box in Fig. 6(b) to ensure the linear additive relation.
For the panel image generation, a 3D scene was created using a 3D rendering and modeling software 3ds Max. The corresponding spatio-angular light ray distribution was prepared in a form of 7 × 7 orthographic view images using a software POV-RAY. From the 7 × 7 orthographic views, images for three panels in the stack were generated using simulated algebraic reconstruction technique (SART) [15].
Figure 7 shows the 3D scenes used in the experiment. For the conventional multi-layer light field display without polarization dependent internal reflection, two objects were located at 0 mm and −46 mm depths. For the proposed scheme with polarization dependent internal reflection, they were located at 0 mm and −6 mm. Note that the polarization of the object at −6 mm was controlled by the PCP such that it undergoes double internal reflections between the HM and the RP of d = 20 mm gap, making its apparent depth be −46 mm, same as the conventional multi-layer light field display case. Figure 8 shows the generated panel images for the conventional and the proposed cases. These images were loaded to the corresponding panels in the panel stack to reconstruct the spatio-angular light ray distribution, displaying 3D images.
Fig. 7 3D scene used for experiment (a) Conventional scheme (b) Proposed scheme with polarization dependent internal reflection.
Fig. 8 Generated panel images for (a) Conventional multi-layer display and (b) Proposed multi-layer display.
Figure 9 shows reconstructed 3D images which were captured using a camera from different observing directions. In the conventional multi-layer light field display case, it is shown that the object at −46 mm is out of the depth range and thus severely blurred, while other object at 0 mm is reconstructed clearly. On the contrary, both objects are displayed successfully with proper motion parallax in the proposed method. Therefore the depth enhancement principle of the proposed method can be confirmed.
Fig. 9 Experimental result (a) Conventional multi-layer display and (b) Proposed multi-layer display.
Although the principle is verified by the experimental result, it is also observed that the proposed system exhibits considerable ghost images and color artifact. Figure 10 shows the causes of these two flaws. The ghost images come from low extinction ratio of the RP. Suppose that the transmission and the reflection polarization directions of the RP are x and y, respectively, with corresponding transmittance tx (tx = 1 for ideal) and reflectance ry (ry = 1 for ideal). Assuming that the RP does not have any absorption, the intensities of the desired images (‘A’ and ‘B’ in Fig. 10) and the ghost images (‘A′’ and ‘B′’ in Fig. 10) are given by IA = Iotx, IB = Iorytx/2, IA′ = Io(1-tx)(1-ry)/2, and IB′ = Io(1-ry), where Io is the intensity of the incoming light after the HM. In our experimental implementation, tx and ry are approximately 0.90 and 0.88 at 550nm wavelength, which gives IA = 0.90Io, IB = 0.40Io, IA′ = 0.01Io, and IB′ = 0.12Io. Therefore, the ghost image of the 3D images of the internal reflection polarization, i.e. B′, has significant intensity in our current implementation. However, considering that tx = 0.90 and ry = 0.88 parameters of the RP used in our experiment are far from the ideal values, the ghost image is expected to be reduced by using the RP with improved parameters.
Fig. 10 Causes of the image artifacts in the experimental results (a) Ghost artifact, (b) Color artifact.
The color distortion artifact mainly comes from the color filter of the PCP in our current implementation. In the proposed method, the PCP only needs to switch the polarization, and hence a monochromatic LC panel without the color filter is adequate. In our implementation, however, a color LC panel with the color filter was used because the monochromatic panel was not available at the time of the implementation. Figure 10(b) illustrates how the redundant color filter of the PCP distorts the color of the 3D images. Note that the RGB order of the PCP is reversed in Fig. 10(b) as the LC panel used as the PCP was inverted to match the polarization direction with the panel stack in our implementation. As shown in Fig. 10(b), the color filter of the PCP attenuates different colors for different ray directions, giving color distortion. However, this color artifact caused by the color filter of the PCP can be readily eliminated by using the monochromatic LC panel as the PCP. Note that the wavelength dependency of the optical plates added in the proposed method also contributes to the color artifact, and hence they need to be reduced as well.
Besides the ghost image and the color artifact, the reduced and unbalanced brightness is another problem. The use of HM reduces the brightness by 1/2 for direct pass polarization and 1/4 for double internal reflection polarization. This brightness loss needs to be compensated by controlling the brightness of the panel images properly. Note that this brightness loss of the proposed method is still less than that of the conventional multi-layer display with double number of the LC panels to achieve the same depth range as the LC panel transmittance is usually low. The alignment errors of the RP and the HM in the proposed method are another consideration point. The gap error Δd between the RP and the HM shifts the apparent depth of the 3D images that undergoes the double internal reflection by 2Δd, inducing the depth error. The out-of-plane rotation of the RP or the HM causes slanted reflection, which results in spatial and angular, i.e. parallax, shift of the 3D images of the double internal reflection. Therefore the alignment of the RP and the HM needs to be controlled carefully in the proposed method. Finally, the time-multiplexing of the proposed method requires two-times higher frame rate than the conventional multi-layer displays. However, the frame rate of recent LC panels exceeds 240Hz, making the time-multiplexing requirement of the proposed method not highly critical.
5. Conclusion
We propose the depth enhancement technique for the multi-layer light field display. The multi-layer light field display presents 3D images by reconstructing the spatio-angular light ray distribution using a stack of the transmission type panels. In spite of many advantages especially for small depth images, the spatio-angular spectral support of the multi-layer light field display converges to that of the conventional autostereoscopic displays like multi-view or integral imaging for large depth images, limiting the available depth range. The proposed method in this paper adds an optical configuration on top of the conventional multi-layer light field display to give polarization dependent internal reflection. For one polarization state, the light undergoes double internal reflections, increasing apparent distance from the observer. By multiplexing two polarization states, the depth range of the multi-layer light field display can be doubled. The experimental result verifies the principle of the proposed method successfully.
Acknowledgment
This work was supported by the IT R&D program of MKE/KEIT. [KI001810035337, A development of interactive wide viewing zone SMV optics of 3D display]
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