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We propose a polarization distributed depth map (PDDM) which can be used in a depth-fused three-dimensional (DFD) display. PDDM is obtained from a conventional depth map using a polarization switching device and shows different polarization states for each pixel depending on the depth position of corresponding pixel. The proposed DFD system using PDDM is composed of three devices which are projection-type display, polarization switching device, and polarization-selective scattering screens. We demonstrate the feasibility of our proposal by the experiment.
©2011 Optical Society of America
1. Introduction
The great success of the three-dimensional (3D) movie ‘Avatar’ in 2009, which resulted in gross revenue of about 2.7 billion dollars, brought the 3D epoch to the display field. Currently, stereoscopic type 3D displays are dominant in TV and movie applications. Stereoscopic 3D displays are usually based on flat panel displays for instance liquid crystal displays (LCDs) or organic light emitting diodes (OLEDs). Rapid improvement of LCD and OLED over the past few years realized high quality 3D displays. Because only two different images are required for providing 3D images in a stereoscopic method, just adopting simple equipment such as shutter glasses can convert a conventional display into a 3D display. As a result, 3D images as good as two-dimensional (2D) images shown in current high definition TVs can be easily achieved using stereoscopic method. However, stereoscopic displays are not suitable for mobile or public signage applications although they provide high quality 3D images and have a lot of merits. It is because auxiliary equipment is necessary for observing 3D images. The inconveniences arisen from wearing, especially for those who already wear glasses, and carrying auxiliary equipment can seriously limit the flexibility in application.
Autostereoscopic display, on the other hand, which is considered as a next generation 3D display, is more flexible in applications because 3D images can be observed without any special equipment. Depth-fused three-dimensional (DFD) display is one of autostereoscopic display which is composed of two layers of 2D displays [1]. DFD displays can show 3D images between their two display layers by adjusting the luminance ratio of the layers. Since DFD method can satisfy not only binocular disparity but also accommodation cues, it provides more natural and comfortable 3D images [2,3]. In previous researches, various kinds of DFD displays are proposed including compact type and projection-type DFDs, which show great expandability of DFD displays [1,4–6]. Also, DFD system has advantage in 3D broadcasting by adopting depth-image-based rendering (DIBR) because its data format can be converted into a 2D image, a depth image, or a depth map, which adds only one-third times of more data in conventional 2D image data [7]. Moreover, real-time 3D recording and playing will be simply achieved using depth camera which obtains depth images as well as 2D images at the same time [8].
In this paper, we propose a polarization distributed depth map (PDDM) which can be directly used for displaying DFD images. PDDM is a 2D image which contains depth information of each pixel as a form of polarization state. PDDM is highly compatible with a DIBR method and a depth camera system because it is based on a depth map. When PDDM is projected onto polarization-selective scattering film, only a part of light will be scattered depending on its polarization state. As a result, luminance modulation of multiple layers will be achieved by proper adjustment of polarization. We demonstrate DFD system using PDDM which shows feasibility of our proposal.
2. Principle
2.1 Polarization distributed depth map
Depth map is a monochromatic 2D image which expresses depth information of each pixel as a grey level. Typical 8-bit depth map can represent 256 different depth positions. Usually, depth map has its corresponding 2D image which shows color information of each pixel. PDDM is a 2D image containing both color and depth information of each pixel. It can be obtained by combining color and depth image using polarization switching device. Polarization switching device uses a liquid crystal which rotates polarization states due to its anisotropic optical property. When liquid crystal is combined with thin-film-transistor array, which enables pixel-by-pixel control of polarization states, it can convert a typical depth map into a PDDM. Actually, the principle of polarization switch is identical to that of the LCD. LCD with analyzer and color filter removed can be used as a polarization switching device. In a typical LCD, luminance of each pixel is chosen by the rotation of polarization. However, if the analyzer is removed from LCD, all pixel will have a same luminance while polarization state of each pixel will be various depending on the given pixel information. Figure 1 shows the schematic diagram of conversion process of PDDM. If a depth image is displayed instead of displaying color image, depth information will be added when a 2D image passes through a polarization switching device.
2.2 Property of polarization selective scattering film
PDDM itself has no difference with 2D images because human eye cannot distinguish the difference in polarization. In order to properly observe a depth distribution of a PDDM, either polarizer or polarization-selective scattering film is required. Specific depth of a 2D image will be expressed as the brightest part of image when a PDDM is observed through a polarizer. A similar process happens when a polarization-selective scattering film is used. However, while a polarizer blocks the perpendicular polarization to its optical axis, a polarization-selective scattering film scatters the perpendicular component. Figure 2 shows the characteristic of polarization-selective scattering film.
If polarization-selective scattering films are stacked with optical axis progressively rotated, PDDM will be gradually imaged on each layer according to the given depth information which can be regarded as a multilayered 3D display. Several multilayered 3D displays have been reported based on the after imaging effect of human vision using a high speed switching device [9–11]. Compared to the previous systems which show degradation in a refreshing rate of image, multilayered display based on DFD using a PDDM is suitable for displaying moving pictures.
Imajor (Teijin DuPont films, Japan) film is one of polarization-selective scattering film. However, although the incident light is parallel to its optical axis, about 14% of light is leaked and scattered. We analyzed the property of Imajor films in order to use those films for demonstrating experimental DFD system using PDDM.
2.3 Simulation of perceived depth
In order for a proper modulation of polarization, we analyze the characteristic of polarization switching device and Imajor film. Both scattering and transmitting properties of Imajor film are measured using photo-spectrometer (CS-100A and CA-210; Konica Minolta). Also, the characteristics of polarization switching device are analyzed.
The ratio of light passing through a polarizer is proportional to the cosine squared of an angle difference between the incident polarization and the optical axis of polarizer. Using a similar process, the transmittance and scattering ratio of polarization-selective scattering film can be calculated. However, in the case of Imajor film, which is used in experimental system, leakages are observed on both transmittance and scattering states. We estimated the leakage from the angular scattering characteristics of Imajor film. The leakage at the scattering state is about 3% and at the transmitting state 14% of perpendicularly polarized lights are scattered. Based on these results, we calculated the scattering ratio of Imajor films when they are used in a two-layered DFD system. In a two-layered DFD system using PDDM, the angle difference of optical axis between two Imajor films are set to 90 degrees in order to maximize the expressible depth range. Figure 3 (a) shows the result of the calculation.
Fig. 3 Simulation of polarization scattering film and polarization switching device (a) scattering ratio of Imajor films in two-layered DFD system, (b) characteristic of angular rotation according to given gray level in polarization switching device, (c) perceived depth in a two-layered DFD system using PDDM
For the polarization switching device, we use a conventional LCD monitor with slight modification. In the case of a typical LCD monitor, luminance of each gray level is adjusted to follow the 2.2 gamma curve. Using this polarization modulating property, we calculate the relation of gray level and corresponding angular rotation of polarization as shown in Fig. 3 (b).
According to the analysis above, we can calculate the represented depth position of DFD system using PDDM. The relation between gray level of depth map and represented depth position is shown in Fig. 3 (c). We find that the gray level of depth image is not linearly proportional to the depth position. Consequently, we expect that proper adjustment of gray level of depth map will be required for a correct depth representation.
3. Experiment
3.1 Comparison between real object and fused image in DFD system
In order to compare the simulated result with a real perceived depth, we carry on an experiment which measures the real depth position of fused image in a DFD system. Simple DFD system consisting of two layers of Imajor is used to generate the fused image. The gap between two layers is set to 2cm. 2cm × 2cm square image is used for a fused image and a random dot pattern is located around the fused image. The random dot pattern can move back and forth with mechanical translating stage. The luminance ratio of front and rear Imajor film is controlled by polarization switching device. The polarization switching device is obtained from a typical LCD monitor by removing the black light unit and the front polarization film. By changing the gray level of polarization switching device, the fused image moves back and forth.
In the experiment, the random dot pattern is placed in a specific location, i.e., 0, 5, 10, 15, and 20 mm from the rear layer. The distance between a subject and the DFD system is about 80cm. Subjects are supposed to find the nearest location of the fused image by changing the gray level. The location of random dot pattern is randomly chosen and current gray level is not informed to the subject. The schematic diagram of the experiment is shown in Fig. 4 .
Fig. 4 Comparison of depth position (a) experimental setup, (b) schematic diagram of depth position measurement
For the reference, we measure the luminance of the front and rear layer in the same condition and calculate the depth position. However, in order to avoid the incorrect measurement caused by overlapping of two layers, measuring point is located 60 degrees off the front. The Fig. 5 (a) shows the result of luminance distribution of the front and rear layer along with the given gray level of depth map. We should remark that the luminance characteristics from the front view will be different, because angular scattering property of the film changes along the incident polarization.
Fig. 5 Result of depth comparison experiment (a) luminance properties of front and rear layer, (b) perceived depth by subjects
Four subjects have participated in the experiment. Two of the subjects do not have any knowledge about a DFD method, while the others have an experience of watching DFD system. The result is presented in Fig. 5 (b) as dashed lines. Solid lines in Fig. 5 are calculated using the measurements above and the simulated value based on section 2.3. The general tendency of result follows the calculated value (light blue line) in rear half depth position, while it fits better to the result in the front half simulated (dark blue line). Subjects claim that they clearly observed the fused image moving back and forth. However, they have some difficulties in finding exact location of the fused image in the given experimental setup, especially in the front half region. We expect that more precise analysis of Imajor film, for example, angular scattering property will provide better estimation.
3.2 DFD system using PDDM
The best advantage of DFD system using PDDM is the simple configuration system. Even if in the case of designing a multi layered DFD system, only a few more layers of polarization-selective scattering film is required. Here, we demonstrate two-layered DFD system using PDDM. Figure 6 shows the experimental system.
The experimental system is composed of a projection-type display, a polarization switching device, and two layers of Imajor films. Since our system exploits polarization as a PDDM, a digital light processing (DLP) type projector is preferred to a LCD-type projector. We use a LED projector which has resolution of 1024(h) × 768(v). In front of the projection-type display, convex lenses are located in order to reduce the projection distance and the size of projected image. The projection distance from the projector to the polarization switching device is 20 cm. The gap between two Imajor layers is chosen to 10mm considering the working distance of projection-type display. The effective screen size is 13.3cm × 10cm (width × height). For a polarization switching device, 8.9-inches LCD monitor with 1024(h) × 600(v) resolution is adopted (N089L6-L02; Chi Mei Optoelectronics). It can display 262,144 colors, which implies a capability of 6-bit depth modulation. The back light unit and the front polarization film of the LCD are removed. The resolution of projected image and depth image does not match in this system. However, it does not severely degrade the quality of image because expressible depth range is rather small in this system. One layer of Imajor film is attached on the polarization switching device and is used as a rear layer. The front layer is located 1 cm in front of the rear layer.
4. Result
The experimental results are shown in Fig. 7 . The letter ‘KHU’ is projected but the added depth information have three different values. The first three images are side view of DFD images which show the different locations of imaging along with the given depth map. The remaining three images show proper fusion of front and rear image. In the case of Fig. 7 (a), all letters are imaged on the front layer while they are imaged on the rear layer in the case of Fig. 7 (b). Each letter in Fig. 7 (c) has a different depth position each other. The front views of the results show correct fusion of front and rear images as shown in Fig. 7 (d) ~(e).
Fig. 7 Result of experimental setup (a) letters imaged on front layer, (b) letters imaged on rear layer, (c) letters imaged on both front and rear layer, (d) ~(f) front view of (a) ~(c)
Example of DFD image with continuous depth is shown in Fig. 8 . The side view of DFD image without mapping a 2D image shown in Fig. 8 (b) illustrates the separation of the projected image according to the depth map. It is somewhat similar to the process of DIBR but happens in the real world. The 3D object is created and extends over the Imajor film layers. And then it is mapped with the 2D textures as shown in the result figures.
5. Conclusion
We have analyzed a PDDM which is useful in designing DFD system. PDDM is as highly scalable as projection-type displays and has good compatibility with DFD systems. The DFD system using PDDM proposed in this paper shows a simple configuration and is cost competitive especially for the case of configuring a large-sized display which requires an expensive LCD device in the previous method. The proposed system could replace those devices with Imajor films without a significant modification from the current system. Moreover, DFD system using PDDM can be easily expanded to multi-layered 3D display which shows wider depth range. We think that the multi-layered system will overcome the restrictions of DFD displays such as a narrow viewing angle or limited depth expression as shown in the example of DepthCube [10]. We expect that PDDM can be widely applicable in various types of DFD systems.
Acknowledgements
This work was supported by the IT R&D program of MKE/KEIT. [KI002058, Signal Processing Elements and their SoC Developments to Realize the Integrated Service System for Interactive Digital Holograms].
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